Many continuous control tasks have bounded action spaces and clip out-of-bound actions before execution. Policy gradient methods often optimize policies as if actions were not clipped. We propose clipped action policy gradient (CAPG) as an alternative policy gradient estimator that exploits the knowledge of actions being clipped to reduce the variance in estimation. We prove that CAPG is unbiased and achieves lower variance than the original estimator that ignores action bounds. Experimental results demonstrate that CAPG generally outperforms the original estimator, indicating its promise as a better policy gradient estimator for continuous control tasks.