We discuss a globalization scheme for a class of active-set Newton methods for solving the mixed complementarity problem (MCP), which was proposed by the authors in [3]. The attractive features of the local phase of the method are that it requires solving only one system of linear equations per iteration, yet the local superlinear convergence is guaranteed under extremely mild assumptions, in particular weaker than the property of semistability of an MCP solution. Thus the local superlinear convergence conditions of the method are weaker than conditions required for the semismooth (generalized) Newton methods and also weaker than convergence conditions of the linearization (Josephy-Newton) method. Numerical experiments on some test problems are presented, including results on the MCPLIB collection for the globalized version.