under the generalized Khasminskii-type condition were discussed by Mao (2011)

and the theory there showed that the Euler--Maruyama (EM) numerical solutions converge to the true solutions \emph{in probability}. However, there is so far no result on the strong convergence (namely in $L^p$) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao (2015) to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.