Hearing aids are small electronic devices intended to help those with hearing loss improve their hearing ability with the use of advanced audio signal processing techniques and technologies. Usually, in hearing aids, a set of speech enhancement methods are utilized to improve speech signal quality in low signal-to-noise ratio (SNR) environments. In speech processing, Discrete Wavelet Transform (DWT) algorithm and Spectral Subtraction (SS) filter are some of the most commonly used methods today when handling background noise in hearing aids. However, these speech enhancement systems have drawbacks like in DWT, the selective thresholding face problems when applying to distinct types of noise with different frequencies and time scales, and spectral subtraction has a problem with music noise, which affects the denoising performance. In this paper, the Spectral Subtraction (SS) filter and DWT speech enhancement methods are combined to deal with problem faced by DWT selective thresholding techniques against noise of different frequencies and time scales and the musical noise faced by the spectral subtraction filter. We first used spectral subtraction to reduce average noise intensity and then added DWT thresholding for reducing the background noise further. The contemporary methods evaluated using English speech signals taken from CSTR VCTK Corpus database. The objective metrics used to evaluate proposed speech enhancement systems are MSE, SNR, PESQ, and STOI. The proposed speech enhancement algorithm is applied for noise reduction and then compared with conventional algorithms. Experimental results prove that using of the proposed speech enhancement algorithm reduces background noise, improves the SNR of an original speech signal, and improves the final noise reduction performance.