This paper addresses a new kind of neuron model, which has trainable activation function (TAF) in addition to only trainable weights in the conventional M-P model. The final neuron activation function can be derived from a primitive neuron activation function by training. The BP like learning al-gorithm has been presented for MFNN constructed by neurons of TAP model. Several simulation ex-amples are given to show the network capacity and performance advantages of the new MFNN in com-parison with that of conventional sigmoid MFNN. The paper addresses a new kind of neuron model, which has trainable activation function (TAF) in addition to only trainable weights in the conventional MP model. The final neuron activation function can be derived from a primitive neuron activation function by training. learning al-gorithm has been presented for MFNN constructed by neurons of TAP model. Several simulation ex-amples are given to show the network capacity and performance advantages of the new MFNN in com-parison with that of conventional sigmoid MFNN.