Since animals are unable to express their pain in words thus I use the word 'voiceless' for animals making the sentence: animals are voiceless thus can't complaint to anyone; but another use of dumb animal once I read by one of my colleague. I don't think if it sounds good. To me, voiceless is better. Am I right?
It sounds like your intent is to evoke sympathy for animals. In that case, you would use words chosen to remind people of animals' intelligence.
The most traditional word to refer to animals' inability to speak is dumb, but indeed this word is also used to refer to someone who is stupid, so it connotes that animals are far beneath us. This appears to be exactly what you do not want.
You may use the word voiceless, but it would be slightly literary or poetic in its usage (i.e., not common--I have not heard it used in this context). "Voiceless" usually means that someone is trying to articulate something but their actual vocal cords do not work or they are choosing not to use them. This is not technically the case with most animals, but you may use it to present a picture that they are trying to express their pain and can't. It's common to say things that are not technically correct when anthropomorphizing animals and you may want to do that here---I'm not certain of your intent or context.
If it were me I wouldn't try to use one word for it. I'd probably say it the way you have in your question.
Since animals cannot express their pain as we do, we think that...