A k-source N1×N2 nonblocking multicast switching network has N1 input ports and N2 output ports with each port having k independent channels, in which each input channel can perform a multicast connection, i.e. send data simultaneously to multiple output channels, without interrupting existing multicast connections from other input channels. We provide the construction and the routing algorithm of a multi-source nonblocking multicast three-stage switching network. A k-source N1×N2 such a switching network consists of three stages of switch modules (which are k-source multicast switching networks with smaller sizes). It has r1 k-source n1×m switch modules in the input stage, m k-source r1×r2 switch modules in the middle stage, and r2 k-source m×n2 switch modules in the output stage with N1=n1r1 and N2=n2r2. There are exactly k channels (corresponding to one port of k-source switch module) between every two switch modules in two consecutive stages. The nonblocking condition for the multicast network is m > min 1 ≤ x ≤ min  { n 2 - 1 , r 2 }  { ⌊ ( n 1 - 1 k )  x ⌋ + ( n 2 - 1 )  r 2 1 x } A refining approach to further reduce the above m value by reducing m′ (which may start from ( n 2 - 1 )  r 2 1 x ) for the chosen x in the above is also disclosed.