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A three-axis atomic magnetometer employing longitudinal field modulation is demonstrated theoretically and experimentally. The operational condition of this magnetometer is that the longitudinal z-component of the external magnetic field is dominant, which is achieved by applying a bias magnetic field. The longitudinal z-component of the external magnetic field is extracted from the modulation frequency, which tracks the resonance frequency, and the transverse x- and y- components are, respectively, obtained from the quadrature and the in-phase signals of a lock-in amplifier. Through feedback control, the magnitude and direction of an external magnetic field can be measured in real time, and an excellent orthogonality of the three-axis magnetometer response is obtained. By optimizing the parameters of this three-axis magnetometer, a longitudinal field sensitivity of 0.3 ${\rm{pT}/ \rm{Hz}}^{1/ 2}$ and a transverse field sensitivity of 2 ${\rm{pT}/ \rm{Hz}}^{1/ 2}$ are achieved.