In this paper we introduce a new function for image denoising. The new function is simple and continuous. It obtains some advantages from both: the hard-thresholding function and the soft-thresholding function. It overcomes the shortcoming that there is an invariable dispersion between the estimated wavelet coefficients and decomposed wavelet coefficients of the soft-thresholding method. At the same time

this function overcomes the shortcoming of the hard-thresholding method with discontinuous functions. We proof that the new function satisfies the shrinkage condition and has infinite rank continuous derivative. At the same time

it has adaptive character and is suitable for various mathematical processing. These advantages make it possible to construct an adaptive algorithm for image denoising. At last

several numerical experiments show that the proposed new function is very effective and predominant. It gives better performance both in terms of PSNR and in visual quality. Our function can preserve more significant information of original images like edges and details than the soft-thresholding function. At the same time

the images denoised by our function are smoother than those denoised by the hard-thresholding function. It also gives a better MSE performance than two typical methods.