7. Given an increasing sequence of positive integers $a_{1}, a_{2}, \cdots$ satisfying $a_{7}=120$, for any positive integer $n$, we have
$$
a_{n+2}=a_{n+1}+a_{n} \text {. }
$$

Then $a_{8}=$ $\qquad$
7. 194.

From the recurrence relation, we get
$$
a_{7}=5 a_{1}+8 a_{2}, a_{8}=8 a_{1}+13 a_{2} \text {. }
$$

Then $5 a_{1}+8 a_{2}=120$.
Solving this indeterminate equation and given that the sequence is increasing, we get
$$
a_{1}=8, a_{2}=10 \text {. }
$$

Therefore, $a_{8}=8 a_{1}+13 a_{2}=194$.