Both random and interval variables can coexist in a single reliability problem. Such cases could pose a serious challenge for existing reliability analysis methods. In this paper, we present a parallel active learning Kriging method for hybrid reliability analysis under both random and interval variables. The key contribution of the proposed method is developing a parallel active learning strategy that can identify a batch of points at each iteration, and hence parallel computing. This is achieved by proposing a new learning function, called pseudo weighted expected risk function (PWERF), which is based on the use of the expected risk function, an influence function and the joint probability function of basis random variables. Once a predefined stopping criterion is satisfied, the lower and upper-bounds of the failure probability can be estimated from the Kriging model as a surrogate for the true performance function. Two numerical examples are employed to demonstrate the performance of the proposed method in comparison with an existing method.