Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced uncorrelated disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of a heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than is expected for conventional three-dimensional topological insulators. Our theoretical results can also be applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb, and their ternary alloys InAsSb.