Binary neural networks (BNNs), where both activations and weights are radically quantized to be {-1, +1}, can massively accelerate the run-time performance of convolution neural networks (CNNs) for edge devices, by computation complexity reduction and memory footprint saving. However, the non-differentiable binarizing function used in BNNs, makes the binarized models hard to be optimized, and introduces significant performance degradation than the full-precision models. Many previous works managed to correct the backward gradient of binarizing function with various improved versions of straight-through estimation (STE), or in a gradual approximate approach, but the gradient suppression problem was not analyzed and handled. Thus, we propose a novel gradient corrected approximation (GCA) method to match the discrepancy between binarizing function and backward gradient in a gradual and stable way. Our work has two primary contributions: The first is to approximate the backward gradient of binarizing function using a simple leaky-steep function with variable window size. The second is to correct the gradient approximation by standardizing the backward gradient propagated through binarizing function. Experiment results show that the proposed method outperforms the baseline by 1.5% Top-1 accuracy on ImageNet dataset without introducing extra computation cost.