An unstructured triangular mesh is successfully applied to the static simulations of air bearing sliders due to its flexibility, accuracy and mesh efficiency in capturing various complex rails and recess wall regions of air bearing surface, as well as fast simulation speed. This paper introduces a new implicit algorithm with second order time accuracy for the time-dependent simulations of the slider dynamics and available for the unstructured triangular mesh. The new algorithm is specially developed for the finite volume method. Since the algorithm has second order time accuracy, it provides the flexibility of applying various time steps while guaranteeing the numerical accuracy and convergence. Moreover, the unstructured triangular mesh is highly efficient and fewer nodes are used. Finally, due to the small variation of flying attitude between two neighboring time steps, it is especially efficient for iteration methods which are used in the finite volume method. As a result, the algorithm shows very fast speed in time-dependent dynamic simulations. Simulation studies are conducted on the flying dynamics of a thermal flying-height control slider after external excitations. The simulation results are compared with the simulation results obtained by the rectangular mesh based on the finite element method. It is observed that the simulation results are well correlated. The fast Fourier transform is also employed to analyze the air bearing frequencies. It is indicated that the new algorithm is of high efficiency and importance for time-dependent dynamic simulations.