A holdup problem on workers' skill investment can arise when employers adopt discriminatory hiring norm to extract higher than socially optimal profit. When hiring priority is determined by both productivity-dependent (skill level) and -independent characteristics (discrimination), skill investment decision becomes strategic between the discriminated and favored group. We consider frictional markets with either posted or bargained wage (fixed sharing rule). With posted wage, depending on market tightness there may be equilibrium or multiple equilibria on skill investment. With discriminatory hiring, if in equilibrium both groups stay high skilled, both are worse off and firms better off; In any equilibrium where one group underinvest, the other group remain high skilled and are better off, while firms are worse off with discrimination. With bargained wage, similar equilibrium where the favored group underinvest exists, and firms incur cost for an intermediate range of bargaining power when they discriminate.