This paper proposes a low power speech recognition processor based on an optimized DNN with precision recoverable approximate computing. In order to accelerate and improve energy utilization of DNN, an approximate multiplier based on cartesian genetic programming with weight pre-classification and mismatch compensation is proposed. A partial retraining scheme based on approximate noise is proposed to recover the accuracy loss caused by approximate computing.Implemented under 22nm, the proposed processor can support the recognition of 10 keywords under signal-to-noise ratios (5dB∼clean), while the recognition accuracy is up to 89.82% and power consumption is 8.6µW.