Is the sentence correct?

Not really--it seems to assume that the spread of the religion will reduce suffering, which is not demonstrated--so that makes it not logically founded. Also, the locution "of as many people" is a fragment. The common English locution would be "of as many people as possible." Therefore, I would consider it neither logical nor grammatically correct. One might write: "ABC religion is being spread quickly, its adherents believing that this will reduce the suffering of as many people as possible.

Hi Setanta,
I appreciate very much your detailed and logical reply, and your showing me how the sentence should be rewritten to make it logical.

You're welcome, Miss Tan. It is a pleasure to talk with you.