In a one-dimensional spinless p-wave superconductor with coherence length ξ, disorder induces a phase transition between a topologically nontrivial phase and a trivial insulating phase at the critical mean-free path l=ξ/2. Here, we show that a multichannel spinless p-wave superconductor goes through an alternation of topologically trivial and nontrivial phases upon increasing the disorder strength, the number of phase transitions being equal to the channel number N. The last phase transition, from a nontrivial phase into the trivial phase, takes place at a mean-free path l=ξ/(N+1), parametrically smaller than the critical mean-free path in one dimension. Our result is valid in the limit that the wire width W is much smaller than the superconducting coherence length ξ.
