PC Amar Tasaddiq Hussain, 29, is one of three men accused of conspiring to make a "false and malicious" 999 call to West Midlands Police.
He denies two counts of conspiracy to pervert the course of justice.
Adil Bashir, 26, and Muhammad Ali Sheikh, 31, have also denied the charges at Stafford Crown Court.
More on this and other Birmingham stories
Prosecutor Simon Davis said the bogus call about the kidnap plot on 8 December 2014, and another two calls made earlier on 27 September about an alleged sham marriage, were staged to target two members of a religious group; Faisal Sami and Irfan Ul-Haq, because of a "personal grudge".
The court heard Mr Hussain wanted to be the head of security at the Dawat-e-Islami faith group where Mr Sami was the leader.
This sparked the three defendants to plot a "course of conduct intended to undermine Ul-Haq and, in turn, a friend of his called Faisal Sami", said Mr Davis.
The court heard from Irfan Ul-Haq from Pakistani via video link, who was arrested after counter-terrorism police raided a tyre business in Walsall as part of the investigation, and he was deported for immigration offences.
Mr Ul-Haq claimed to have been friends with Mr Hussain for seven years and knew him as Amir.
"Amir wanted to become head of security department. He wanted to be security head," he said, referring to the Dawat-e-Islami group.
Mr Hussain, from Yardley, who is suspended from duty, was charged with Mr Bashir of Small Heath and Mr Sheikh from Bordesley Green. All three deny the charges.
The trial continues.

Voting was extended three times as crowds reportedly flocked to polling stations. Turnout was said to be high.
Iranians have been electing a new parliament and Assembly of Experts, a clerical body that appoints the Supreme Leader.
Reformists are hoping to gain influence in the conservative-dominated bodies.
But of 12,000 people who registered as candidates, only half were allowed to stand, including  just 200 moderates.
The outcome could affect reformist President Hassan Rouhani's chances of re-election in 2017.
What is the Assembly of Experts?
Iran elections: Five things to know
Elections highlight divisions
Punchy politics on social media
Supreme Leader Ayatollah Ali Khamenei called for a big turnout to "disappoint" the country's enemies.
"Whoever likes Iran and its dignity, greatness and glory should vote," he said after casting his ballot.
State TV said polling stations had closed at 23:45 (20:15 GMT), more than five hours after the scheduled closing time of 18:00.
The parliamentary elections are to choose 290 MPs for four-year terms.
Voters will also select 88 clerics to the Assembly of Experts, who serve eight-year terms.
Members of the new Assembly might end up choosing the successor to Ayatollah Khamenei, who is 76 and has suffered ill-health.
Some 55 million people were eligible to vote.
BBC Persian's Ali Hamedani says the economy has been a key issue in this election.
With sanctions lifted and Western investors beginning to return to Iran, there are high hopes for an improvement in daily life, he says.
Reformists and moderates say they are targeting greater foreign investment which, our correspondent says, will drive jobs for young people.
More than half of Iranians are under 35 but the youth unemployment rate is 25%, more than two and a half times the national average.
However, conservatives say strong economic growth is more likely to come from domestic production in what they describe as a "resistance economy" that draws on the ideals of the country's 1979 Islamic Revolution.
Results for the Assembly of Experts are expected over the weekend.
The results of the parliamentary election could take longer and it is likely to go to a second round in April.
Candidates need 25% of the vote to win outright and there are an average of 17 candidates per seat.
A police officer tried to incriminate two men over a "personal grudge" by faking a so-called "IS kidnap" of an officer, a court has heard.
[NEXT_CONCEPT]
Polls have closed in Iran's first election since a deal with world powers over the country's nuclear programme and the lifting of sanctions.