Artificial-Neural Network (ANN) is a complex network system composed of many simple elements connected extensively each other and can be regarded as a simulation or abstraction of biological neural system. Multi-Layer Network (MLN) is one of the most important ANN. A essential algorithm to train MLN is BP (Back-Propagation) algorithm. Based on BP algorithm, a hgih-speed algorithm-train MLN layer-by-layer algorithm is proposed with main points:4) train MLN layer-by-layer instead of all together; b) giving instruction to hidden units; c) giving appropriate "energy function' according to specific Problems; d) preserving the merits of BP algorithm. The simulation results increase by orders of magnitude in training-speed. This algorithm applies also some research on running mechanism of MLN.