We demonstrated a TEM00 mode orthogonal dual-slab Yb:KG(WO4)2(Yb:KGW) laser oscillator with high average power. Polarization anisotropy of thermal lenses was investigated and alleviating the astigmatism based on orthogonal dual-slab. In addition, the laser polarization was directly controlled by adjusting the net gain of the two crystals. The maximum output power was highly enhanced compared with single crystal due to effective thermal distribution. For an absorbed pump power of 52.4 W, this oscillator delivered an average power of 26.5 W, corresponding to an optical-to-optical conversion efficiency of 50.6%. Meanwhile, the ellipticity of the output laser was optimized to 0.940. Nearly diffraction-limited beam quality was measured to be M x2 = 1.19 and M y2=1.18.