The conventional linear polarizer only allows the electric component parallel to the polarizer axis to pass through whereas prohibits the vertical component. We propose that a specially-designed single-layer plasmonic polarizer can couple both parallel and vertical electric components to the transmission, thus breaking the classical law of Malus. A variety of anomalous polarization effects, such as the asymmetric polarization-angle dependence, enhanced polarization filtering with wide polarization angle, and tunable polarization rotation from 0 o to 90 o , can be resulted. To understand the effects, the generalized law of Malus, originating from the superposition principle, has been presented and analyzed. This provides a basis for studying the interference-type plasmonic polarizers, where the interference effect and polarization effect are combined together. The difference between the plasmonic and conventional polarizers is of both fundamental and practical interests.