This paper proposes an a priori signal-to-noise ratio (SNR) estimator using an air-conduction (AC) and a bone-conduction (BC) microphone. Among various ways of combining AC and BC microphones for speech enhancement, it is shown that the total enhancement performance can be maximized if the BC microphone is utilized for estimating the power spectral density (PSD) of the desired speech signal. Considering the fact that a small deviation in the speech PSD estimation process brings severe spectral distortion, this paper focuses on controlling weighting factors while estimating the a priori SNR with the decision-directed approach framework. The time-frequency varying weighting factor that is determined by taking a minimum mean square error criterion improves the capability of eliminating residual noise and minimizing speech distortion. Since the weighting factors are also adjusted by measuring the usefulness of the AC and BC microphones, the proposed approach is suitable for tracking the parameter even if the characteristic of environment changes rapidly. The simulation results confirm the superiority of the proposed algorithm to conventional algorithms in high noise environments.