A new stable numerical method, based on Chebyshev wavelets for numerical evaluation of Hankel transform, is proposed in this paper. The Chebyshev wavelets are used as a basis to expand a part of the integrand, r f(r), appearing in the Hankel transform integral. This transforms the Hankel transform integral into a Fourier-Bessel series. By truncating the series, an efficient and stable algorithm is obtained for the numerical evaluations of the Hankel transforms of order ν > −1. The method is quite accurate and stable, as illustrated by given numerical examples with varying degree of random noise terms εθ_i added to the data function f(r), where θ_i is a uniform random variable with values in [−1,1]. Finally, an application of the proposed method is given for solving the heat equation in an infinite cylinder with a radiation condition.