The intensive computation of Automatic Speech Recognition (ASR) models obstructs them from being deployed on mobile devices. In this paper, we present a novel quantized Winograd optimization pipeline, which combines the quantization and fast convolution to achieve efficient inference acceleration on mobile devices for ASR models. To avoid the information loss due to the combination of quantization and Winograd convolution, a Range-Scaled Quantization (RSQ) training method is proposed to expand the quantized numerical range and to distill knowledge from high-precision values. Moreover, an improved Conv1D equipped DFSMN (ConvDFSMN) model is designed for mobile deployment. We conduct extensive experiments on both ConvDFSMN and Wav2letter models. Results demonstrate the models can be effectively optimized with the proposed pipeline. Especially, Wav2letter achieves 1.48* speedup with an approximate 0.07% WER decrease on ARMv7-based mobile devices.