Compressed hydrogen-rich compounds have received extensive attention as appealing contenders for superconductors. Here, we found several stable hydrides YZrH6, YZrH8, YZr3H16 and YZrH18, and a series of metastable clathrate hexahydrides in the systematic investigation of Y-Zr-H ternary hydrides under pressure. Electron-phonon coupling calculations indicate that they all exhibit high temperature superconductivity and perform better than the binary Zr-H system. YZrH6 can maintain dynamic stability down to ambient pressure and keep a critical temperature (Tc) of 16 K. The stable YZrH18 and metastable Y3ZrH24 with high hydrogen content exhibit high Tc of 156 K and 185 K at 200 GPa, respectively. Further analysis shows that the phonon modes associated with H atoms contribute significantly to the electron-phonon coupling. The hydrogen content and the stoichiometric ratio of Y and Zr closely affect the density of states at the Fermi level, thereby affecting the superconductivity. Our work presents an important step toward understanding the superconductivity and stability of transition metal ternary hydrides.