Wall-clock convergence time and communication rounds are critical performance metrics in distributed learning with parameter-server setting. While synchronous methods converge fast but are not robust to stragglers; and asynchronous ones can reduce the wall-clock time per round but suffers from degraded convergence rate due to the staleness of gradients, it is natural to combine the two methods to achieve a balance. In this work, we develop a novel asynchronous strategy that leverages the advantages of both synchronous methods and asynchronous ones, named adaptive bounded staleness (ABS). The key enablers of ABS are two-fold. First, the number of workers that the PS waits for per round for gradient aggregation is adaptively selected to strike a straggling-staleness balance. Second, the workers with relatively high staleness are required to start a new round of computation to alleviate the negative effect of staleness. Simulation results are provided to demonstrate the superiority of ABS over state-of-the-art schemes in terms of wall-clock time and communication rounds.