The key aim of this paper is to show the strong convergence of the truncated EulerMaruyama method for neutral stochastic differential delay equations (NSDDEs) with Markovian switching (MS) without the linear growth condition.We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under the local Lipschitz condition plus Khasminskii-type condition.We also study its strong convergence rates at time T and over a finite interval[0,T].Some numerical examples are given to illustrate the theoretical results.