A symmetric hybrid electromagnetic-circuit simulator based on the extended time-domain finite element method (FEM) is presented for the simulation of microwave devices embedded with linear/nonlinear lumped circuits. The distributive portion of the device is modeled by the time-domain FEM to generate an electromagnetic subsystem, while the embedded lumped circuits are analyzed by a SPICE-like transient circuit solver to generate a circuit subsystem. A symmetric global system for both the electromagnetic and circuit unknowns is then established by combining the two fully discretized subsystems through coupling matrices to model their interactions. For active devices, the resulting global electromagnetic-circuit system usually includes nonlinear equations, and thus is solved by a solution algorithm carefully designed to handle nonlinearity. The proposed simulator significantly extends the capability of the existing time-domain finite element solver to model more complex and active devices such as microwave amplifiers. Numerical examples are presented to validate the algorithm and demonstrate its accuracy and applications.