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The subject of this article is an analytic approximate method for a class of stochastic differential equations with time-dependent delay, with coefficients that do not necessarily satisfy the Lipschitz condition nor the linear growth condition but they satisfy the polynomial condition. More precisely, it is assumed that equations from the observed class have unique solutions with bounded moments, their coefficients satisfy the polynomial condition and some derivatives of the specific order of the drift and diffusion coefficients are uniformly bounded. Approximate equations are defined on partitions of the time interval and their coefficients are Taylor approximations of the coefficients of the initial equation up to arbitrary derivatives. It is shown that the solutions of the approximate equations converge in thesense and almost surely toward the solution of the initial equation and the rate of the convergence is given.

A Taylor method for stochastic differential equations with time-dependent delay via the polynomial condition