This paper develops a class of general one-step discretization methods for solving the index-1 stochastic delay differential-algebraic equations.The existence and uniqueness theorem of strong solutions of index-1 equations is given.A strong convergence criterion of the methods is derived,which is applicable to a series of one-step stochastic numerical methods.Some specific numerical methods,such as the Euler-Maruyama method,stochastic θ-methods,split-step θ-methods are proposed,and their strong convergence results are given.Numerical experiments further illustrate the theoretical results.