This paper deals with the semi-implicit Euler methods for initial value problems of nonlinear neutral stochastic pantograph equations. Convergence of the semi-implicit Euler methods in the mean square sense for the system is investigated. It is shown that the semi-implicit Eulermethodsaremean squareconvergent withorder 1/2. Anumerical example illustrates the theoretical results.

neutral stochastic pantograph equations, semi-implicit Euler methods, mean square convergence, consistency.