This work considers the model reduction of linear time-invariant systems with focus on good approximation at a particular frequency. A family of frequency-dependent extended systems preserving some special frequency-dependent properties is constructed first, then the corresponding controllability and observability Lyapunov equations are defined. Finally, those results are used to develop the desired frequency-dependent balanced truncation, which generates the desired reduced-order model with an explicit frequency-dependent approximation error bound. Both continuous-time and discrete-time systems are considered. Several benchmark examples are tested to illustrate the advantage of the proposed frequency-dependent balanced truncation method.