A model based on propagation-rate equations by considering the multi-transverse mode is constructed to describe the amplifier made from seven-core photonic crystal fibers. The output power of the seven eigenmodes in the amplifier infected by the dopant distribution, coupling coefficient and the pump power is discussed using the split-step Fourier algorithm. Mode selection can be realized by the design of dopant distribution and suitable coupling coefficient without the need of other devices. Mode selection may become more convenient due to this method. Moreover, high pump power can contribute to the improvement of the in-phase supermode. These results are helpful for improving the light quality of the amplifier.