NRQCD factorization is currently the most widely used theory to describe heavy quarkonium production. Although NRQCD has got lots of successes, it also faces some notable difficulties right now. A possible reason to explain these difficulties is that, because of soft gluons radiation at the hadronization stage, convergence of velocity expansion in NRQCD is too bad. In the soft gluon factorization, we take into account the soft gluon radiation effect and thus expect to have a much better convergence. The soft gluon factorization may provide a better description for heavy quarkonium production.