We report on the growth, spectroscopic and laser characterization of a novel monoclinic laser crystal, 3.5 at.% Yb, 5.5 at.% In:KLu(WO4)2 (Yb,In:KLuW). Single-crystals of high optical quality are grown by the TSSG method. The absorption, stimulated-emission and gain cross-sections are determined for this material at room temperature with polarized light. The maximum σabs is 9.9×10-20 cm2 at 980.8 nm for light polarization E || Nm. The radiative lifetime of Yb3+ in Yb,In:KLuW is 237±5 μs. The stimulated-emission cross-sections are σSE(m) = 2.4×10-20 cm2 at 1022.4 nm and σSE(p) = 1.3×10-20 cm2 at 1039.1 nm corresponding to an emission bandwidth of >30 nm and >35 nm, respectively. A diode-pumped Ng-cut Yb,In:KLuW microchip laser generates 4.11 W at 1047-1052 nm with a slope efficiency of 78%. Passive Q-switching of a Yb,In:KLuW laser is also demonstrated. The Yb,In:KLuW crystal seems very promising for sub-100 fs mode-locked lasers.