In this paper, we focused on the accelerated modulus-based matrix splitting iteration method for solving nonlinear complementarity problems. A thorough analysis of convergence conditions for the method was conducted. Compared to the work "B. H. Huang, C. F. Ma, Accelerated modulus-based matrix splitting iteration method for a class of nonlinear complementarity problems, Comp. Appl. Math., 37 (2018), 3053–3076", our results achieved three significant improvements: Relaxing the assumptions on matrix splittings, providing an expanded convergence domain for parameter matrix, and simplifying conditions for relaxation parameters. The validity of the theoretical findings was verified by numerical examples.