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Recently, pre-trained Transformer based language models, such as BERT, have shown great superiority over the traditional methods in many Natural Language Processing (NLP) tasks. However, the computational cost for deploying these models is prohibitive on resource-restricted devices. One method to alleviate this computation overhead is to quantize the original model into fewer bits representation, and previous work has proved that we can at most quantize both weights and activations of BERT into 8-bits, without degrading its performance. In this work, we propose MKQ-BERT, which further improves the compression level and uses 4-bits for quantization. In MKQ-BERT, we propose a novel way for computing the gradient of the quantization scale, combined with an advanced distillation strategy. On the one hand, we prove that MKQ-BERT outperforms the existing BERT quantization methods for achieving a higher accuracy under the same compression level. On the other hand, we are the first work that successfully deploys the 4-bits BERT and achieves an end-to-end speedup for inference. Our results suggest that we could achieve 5.3x of bits reduction without degrading the model accuracy, and the inference speed of one int4 layer is 15x faster than a float32 layer in Transformer based model.