Fuzzy random variable is a measurable map from a probability space to a collection of fuzzy variables. In this paper, we first present several new convergence concepts for sequences of fuzzy random variables, including convergence almost sure, uniform convergence, almost uniform convergence, convergence in mean chance, and convergence in mean chance distribution. Then, we discuss the criteria for convergence almost sure, almost uniform convergence, and convergence in mean chance. Finally, we deal with the relationship among various types of convergence.