We describe a fast and accurate method to perform the convolution of a sky map with a general asymmetric main beam along any given scanning strategy. The method is based on the decomposition of the beam as a sum of circular functions, here Gaussians. It can be easily implemented and is much faster than pixel-by-pixel convolution. In addition, Asymfast can be used to estimate the effective circularized beam transfer functions of CMB instruments with non-symmetric main beam. This is shown using realistic simulations and by comparison to analytical approximations which are available for Gaussian elliptical beams. Finally, the application of this technique to Archeops data is also described. Although developped within the framework of Cosmic Microwave Background observations, our method can be applied to other areas of astrophysics.