Your workout seems to be top-heavy; in other words, it works your upper body more than your lower body. Additionally, ther should be a balance between push and pull for a given muscle group. For example, if you do 20 barbell curls (biceps) you ought to also do 20 pull-ups (triceps)- although even then there's a better way.
Are you going for bulk or tone? That is, strength or fat burning? It's highly difficult to do both. Getting a clear idea will help you design a better plan.
Without knowing your height, weight, and max lifts, I think you run the risk of under-exercising or over-exercising. I could be wrong.
If you want, I can help you design a routine that is both short and effective. Free. I don't sell anything. However, as I said, I'll need some information from you.