Continuous-time random disturbances from the renewable generation pose a significant impact on power system dynamic behavior. In evaluating this impact, the disturbances must be considered as continuous-time random processes instead of random variables that do not vary with time to ensure accuracy. Monte Carlo simulation (MCs) is a nonintrusive method to evaluate such impact that can be performed on commercial power system simulation software and is easy for power utilities to use, but is computationally cumbersome. Fast samplings methods such as Latin hypercube sampling (LHS) have been introduced to speed up sampling random variables, but yet cannot be applied to sample continuous disturbances. To overcome this limitation, this paper proposes a fast MCs method that enables the LHS to speed up sampling continuous disturbances, which is based on the Itô process model of the disturbances and the approximation of the Itô process by functions of independent normal random variables. A case study of the IEEE 39-Bus System shows that the proposed method is 47.6 and 6.7 times faster to converge compared to the traditional MCs in evaluating the expectation and variance of the system dynamic response.