<p>We are concerned with the long-time asymptotics of the Cauchy problem for the solution of the nonlocal complex MKdV equation with step-like initial data using the nonlinear steepest descent method. Firstly, following the basic framework of Riemann-Hilbert approach, the basic Riemann-Hilbert problem is constructed, and the reconstruction formula of the solution associated with the Riemann-Hilbert problem is established. Secondly, the one-soliton solution is derived based on the corresponding residue conditions. Finally, we apply a series of transformations to transform the basic Riemann-Hilbert problem into a regular Riemann-Hilbert problem that can be solved, the long-time asymptotics of the solution for the nonlocal complex MKdV equation is obtained in different space-time sectors.</p>