<p>Time crystals constitute a novel phase of matter defined by the spontaneous breaking of time-translation symmetry. Here, we present a scheme to realize a continuous-time crystal of the vibrational phonon in the normal mode of two coupled ultra-cold ions. By utilizing two addressable standing-wave lasers and the adiabatic elimination method, we generate a controllable nonlinear phonon mode with the well-designed efficient linear gain and nonlinear damping. By controlling these parameters to satisfy the phase transition conditions of Hopf bifurcation and limit cycle phase, it exhibits stable dissipative dynamics over timescales significantly longer than the oscillation period, indicating the emergence of continuous time-translation symmetry breaking in the phonon mode, i.e., a phonon time crystal. We further numerically simulate this phonon time crystal by using accessible experimental parameters and also demonstrate its robustness to the initial thermal state and thermalization of phonon mode, spin dephasing, and the control errors of Rabi frequencies. These results provide a practical scheme for observing a time crystal in a nonlinear phonon mode and will advance the research of time crystals.</p>