Aiming at the safety verification problem of a class of stochastic continuous system equipped with both random initial state and stochastic differential equation, a new computation method based on stochastic barrier certificates and initial set selection was proposed. Firstly, the related knowledge and concepts of stochastic continuous system and its safety verification were introduced. Then, it was discussed that how to determine the initial state set for the initial variables obeying several different distributions. The safety verification problem was converted into the polynomial optimization problem by using the method of stochastic barrier certificates according to the selected initial state set. Finally, the sum of squares relaxation method was used to transform the problem into sum of squares programming problem, and the lower bound of safety probability was obtained by using the SOSTOOLS tool. The theoretical analysis and experimental results show that, the proposed method has the complexity of polynomial time and can effectively compute the lower bound of safety probability for stochastic continuous system in unbounded time.