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A high-power single-frequency laser at 671 and 1342 nm is designed and built. We find that for a high power Nd:YVO4 laser, the thermal load of gain medium at 1342 nm lasing is much more stronger than that without lasing, which results in a bistability-like phenomenon on the relation curve between the output power and pump power. Based on the consideration to this special phenomenon, in our design, the cavity parameters are optimized carefully to satisfy the laser stability condition for both cases before and after lasing, the thermal effect of the Nd:YVO4 crystal is mitigated by increasing appropriately the fundamental mode size. The maximal output powers of 2.8 W at 671 nm and 850 mW at 1342 nm are simultaneously achieved.