In this paper, we present a two-stage noise spectra estimation approach. After the first-stage noise estimation using the improved minima controlled recursive averaging (IMCRA) method, the second-stage noise estimation is performed by employing a maximum a posteriori (MAP) noise amplitude estimator. We also develop a regression-based speech enhance system by approximating the clean speech with the estimated noise and original noisy speech. Evaluation experiments show that the proposed two-stage noise estimation method results in lower estimation error for all test noise types. Compared to original noisy speech, the proposed regression-based approach obtains an average relative word error rate (WER) reduction of 65% in our isolated word recognition experiments conducted in 12 real car environments.