Botulinum toxin A (GSK1358820) is a sterile, purified type A botulinum neurotoxin complex. In Japan, 240 units of botulinum toxin A are approved as a maximum dose per administration for upper limb spasticity. This study is planned to evaluate the effectiveness and safety of 400 units of botulinum toxin A which can help to increase the maximum dose per administration to 400 units from 240 units as the treatment with 240 units is considered insufficient in subjects with post-stroke upper limb spasticity. Approximately 120 subjects will be randomized to receive either 400 or 240 units of botulinum toxin A in double blind phase followed by open-label phase in which 400 units of the study treatment will be injected in both the groups. The study period will be up to 52 weeks, consisting of a screening phase up to 4 weeks, minimum 12-week double blind phase (Part 1), maximum 36- week open-label phase (12 weeks per cycle with 3 treatment phases: Part 2, Part 3 and Part 4).