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Over the last few decades, the numerical methods for stochastic differentialdelay equations (SDDEs) have been investigated and developed by many scholars.Nevertheless, there is still little work to be completed. By virtue of thenovel technique, this paper focuses on the mean-square convergence andstability of the backward Euler method (BEM) for SDDEs whose drift anddiffusion coefficients can both grow polynomially. The upper mean-square errorbounds of BEM are obtained. Then the convergence rate, which is one-half, isrevealed without using the moment boundedness of numerical solutions.Furthermore, under fairly general conditions, the novel technique is applied toprove that the BEM can inherit the exponential mean-square stability with asimple proof. At last, two numerical experiments are implemented to illustratethe reliability of the theories.

Mean-square convergence and stability of the backward Euler method for  stochastic differential delay equations with highly nonlinear growing  coefficients