A laser-diode pumped Nd：YVO₄ and Nd：YAG single-longitudinal-mode 589 nm laser is presented. The fundamental waves of 1 064 nm and 1 319 nm simultaneously oscillate through an L type composite resonator. Through intracavity sum-frequency-generation in a KTP crystal （cut at type II phase matching），the single longitudinal mode 589 nm continuous wave is obtained by a birefringent filter which is consisted of a Brewster plate and the KTP crystal. The losses of S- and P- elements of the two fundamental waves are calculated by Jones matrix method. The losses of the first sub-longitudinal modes for 1 064 nm and 1 319 nm are 0.5% more and 2% more than their peak transmission modes respectively. Based on the above mentioned， a single-longitudinal-mode 589 nm laser is realized in experiment. The maximum output power is 58 mW， the amplitude fluctuation is less than 0.36%， and the line width is about 30 MHz. The results show that the birefringent filter technology is effective for single-longitudinal-mode double-wavelength oscillation and sum-frequency-generation lasers.