As the size of models and datasets grows, it has become increasingly common to train models in parallel. However, existing distributed stochastic gradient descent (SGD) algorithms suffer from insufficient utilization of computational resources and poor convergence in heterogeneous clusters. In this paper, we propose a delayed synchronous SGD algorithm with adaptive batch size (ABS-SGD) for heterogeneous GPU clusters. In ABS-SGD, workers perform global synchronization to accumulate delayed gradients and use the accumulated delayed gradients to update parameters. While workers are performing global synchronization for delayed gradients, they perform the computation of the next batch without specifying batch size in advance, which lasts until the next global synchronization starts, realizing the full utilization of computational resources. Since the gradient delay is only one iteration, the stale gradient problem can be alleviated. We theoretically prove the convergence of ABS-SGD in heterogeneous clusters. Extensive experiments in three types of heterogeneous clusters demonstrate that ABS-SGD can make full use of computational resources and accelerate model convergence: When training ResNet18 network with 4 workers, ABS-SGD increases the convergence speed by 1.30x on average compared with the best baseline algorithm.