In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al, which gives generalization of a strong law of large numbers for sums of stationary and ergodic processes to the case of fuzzy random variables. We also generalize the recent result of Kim, which is a strong law of large numbers for sums of levelwise independent and levelwise identically distributed fuzzy random variables.