Magnetized fusion has been used in various inertial confinement fusion concepts to relax ignition requirements. Strong magnetic fields would induce burning asymmetry, which may be usually harmful to the central ignition schemes. However, it could be utilized in some intrinsically asymmetric ignition schemes, such as the traditional fast ignition (FI) scheme and the double-cone ignition (DCI) scheme, in which the hot spots are located at the edge of the compressed fuel. In this paper, an analytical model and a three-dimensional MHD code are developed to study the asymmetric burning propagation and related effects in magnetic fields. It is found that the magnetic field can guide a directional and faster burning propagation along the parallel direction to the B-field by the anisotropic α-particle transport, providing a method to control the burning behavior. The B-field also leads to a faster increase in the hot spot temperature. Simulation shows that 10 kT B-fields, corresponding to the α-particle Hall parameter of H_{α}∼0.5, would increase the hot spot temperature by 38% and the burning propagation speed by 44% in FI and DCI conditions, leading to an 87% increase of the fusion output energy and an 18% increase of hot spot mass. This study could also provide a direct reference for assessing the burning asymmetry in the magnetized ICF schemes.