We analyze M,MMPP/G/1 finite queues with queue-length-threshold (QLT) scheduling policy and Bernoulli schedule where the arrival of type-1 customers (nonreal-time traffic) is Poisson and the arrival of type-2 customers (real-time traffic) is a Markov-modulated Poisson process (MMPP). The next customer to be served is determined by the queue length in the buffer of type-1 customers. We obtain the joint queue length distribution for customers of both types at departure epochs by using the embedded Markov chain method, and then obtain the queue length distribution at an arbitrary time by using the supplementary variable method. From these results, we obtain the loss probabilities and the mean waiting times for customers of each type. The numerical examples show the effects of the QLT scheduling policy on performance measures of the nonreal-time traffic and the bursty real-time traffic in ATM networks.