Digital hearing aid users often complain of difficulty in understanding speech in the presence of background noise. To improve speech perception in a noisy environment, various speech enhancement algorithms have been applied in digital hearing aids. In this study, a speech enhancement algorithm using modified spectral subtraction and companding is proposed for digital hearing aids. We adjusted the biases of the estimated noise spectrum, based on a subtraction factor, to decrease the residual noise. Companding was applied to the channel of the formant frequency based on the speech presence indicator to enhance the formant. Noise suppression was achieved while retaining weak speech components and avoiding the residual noise phenomena. Objective and subjective evaluation under various environmental conditions confirmed the improvement due to the proposed algorithm. We tested segmental SNR and Log Likelihood Ratio (LLR), which have higher correlation with subjective measures. Segmental SNR has the highest and LLR the lowest correlation of the methods tested. In addition, we confirmed by spectrogram that the proposed method significantly reduced the residual noise and enhanced the formants. A mean opinion score that represented the global perception score was tested; this produced the highest quality speech using the proposed method. The results show that the proposed speech enhancement algorithm is beneficial for hearing aid users in noisy environments.