With the continuous miniaturization and rapid increase in the power ratings of an insulated-gate bipolar transistor (IGBT), the exact junction temperature becomes one of the critical performance parameters in evaluating the reliability of the transistor. In this regard, the network topological method is extended to develop a physics-based transient electrothermal model, considering both the 3-D heat complications and the nonlinearity of the thermal parameters, of an IGBT. The network topology method uses the graph theory to describe the network according to the network's geometric structure. Owing to its clear physical meaning, easiness in numerical implementation, and extremely high computational efficiency, the proposed 3-D model and method have an extraordinarily high computational efficiency compared with the finite-element method, and are more accurate than the 1-D lumped RC model, as evidenced by the numerical results as reported.