Noise power spectrum estimation is a fundamental component of speech enhancement. An improved weighted noise power estimation algorithm is proposed in the paper by taking into account the correlation of inter-frequency in the noisy speech. Because of calculating the weighting factor from the time domain and frequency domain smoothed noisy speech, the new presented algorithm can distinguish noise and weak speech more accurately, especially in the weak speech regions following strong speech. The tracking delay and the overestimates are all considerably reduced compared to competitive noise tracking algorithms. Objective experimental results and a subjective comparison show that the improved noise estimation algorithm is preferred to other noise estimation algorithms when integrated in speech enhancement.