A fast algorithm combined with the volume integral equation (VIE) is proposed for analyzing antenna radiation properties in the presence of an arbitrary shaped dielectric radome. The discrete form of the VIE is obtained using the method of moments (MOM). Evaluation of electromagnetic fields is accelerated using the multilevel volumetric non-uniform grid algorithm (MLVNG). The algorithm is based on phase and amplitude compensation of fields which are produced by a bounded volume of source distribution. The compensated field is band-limited function of its coordinates, which allows sampling it on a sparse non-uniform spherical grid at rates proportional to the source volume. Tight sampling rules are suggested in order to reduce the computational complexity of the field evaluation. The computational complexity of the MLVNG algorithm is demonstrated on representative example.