Transverse mode distribution and dopant profile are introduced in propagation-rate equations. An approximate numerical algorithm by multilayer method is presented to calculate the power of amplified signal and amplified spontaneous emission (ASE) in multimode fiber amplifiers. Numerical results of the propagation-rate equations before and after the improvement are compared. It shows that power filling factor is the key indication to describe the transverse mode competition behavior. Dopant profile makes great effect in mode selection and 60%～70% confinement of flat doping is more helpful in high-order mode suppression. ASE significantly drops and SNR increases when the ions are doped more concentrated in the fiber core.