The rate equation model is setup for the signal gain, pump absorption and output noise spectrum of bidirectional erbium-doped fiber amplifier (Bi-EDFA) including numbers of signals, pumps of arbitrary direction, amplified spontaneous emission(ASE) and inherent loss. The influences of erbium-doped fiber length, input signal power, pump style and pump power on the gain characteristis of Bi-EDFA are analyzed. Forward- and backward- noise figure for different pump style versus bidirectional input signal power is investigated. With these results, the optimal design for Bi-EDFAs in optical communication systems and networks can be performed.