This paper presents a non-iterative Kalman filter (NIT-KF) for single channel speech enhancement in nonstationary noise condition (NNC). To adopt NIT-KF with NNC, we address the adjustment of biased Kalman gain through efficient parameter estimation. We introduce an effective noise spectrum tracking method based on decision directed approach (DDA) controlled through a posteriori SNR and speech activity detector (SAD). With the estimated noise spectrum, the spectral over subtraction (SOS) algorithm is employed to the noisy speech; this gives a pre-filtered speech (PFS). The noise variance and LPCs are computed from the estimated noise and PFS, respectively. These are applied to NIT-KF to produce the enhanced speech. It is shown that the adjusted Kalman gain in NIT-KF is effective in minimizing the additive noise effect to an acceptable level. Extensive simulation results reveal that the proposed method outperforms other benchmark methods.