Can I not ask my advisor for recommendation letter if I'm applying for an industry job? I'm currently in my fifth year of my PhD in a molecular biology lab, and I have since last year decided to transition to computational biology field.

My advisor is very much into molecular biology and wasn't happy about my transition. We have fundamental differences in research approaches and he would always force his idea on me. He constantly threatened me not to sign my thesis or to refuse to write a recommendation letter if I don't do exactly as he says. And at this point, I'm just trying to survive grad school, but I'm wondering about the possibility of not having him in my reference list as I don't expect his letter to be very helpful.

My advisor is not very well-known in our field, let alone in any field related to computational biology. Currently I'm trying to improve my programming skills and at the same time fulfill my phd task. I'm thinking that perhaps I can try asking for references from our lab collaborators, my committee or other professors in our department who are much more aquainted in bioinformatics field. 

Any suggestions?
It also sounds like you are considering giving up your doctoral studies. Let me suggest something different. 

It seems to me that you want to try to maximize your future options and realize your potential. I recommend that, for now, you just follow your advisor's direction and get the degree finished and then move on to whatever it is you want to do. You should have plenty of time for a transition to another field after completion and holding the degree will leave you positioned for either an academic or industrial career. 

It may be galling to have to submit, but the advisor has a certain amount of power. Think of him as a door that you need to get through to be a success. 

At that point your immediate problem may go away and he might write you an appropriate letter. 

On the other hand, not having his letter now would probably seem unusual to most employers, so you'd better have a good and honest explanation for why you don't have it. Disagreeing with and advisor isn't an especially valuable trait in the minds of many employers and they may not really understand the situation.