In this article, a class of filtering linear polarization converters based on a single quasi-single-layer triangular resonator unit is proposed. By loading the stub-line and slot lines, the degenerate modes of the single fundamental resonant mode of an isosceles right-angle patch are separated into two for a second-order filtering characteristic, and two additional resonant modes are then generated for the second conversion band. Attributed to the mixed electric and magnetic coupling in the coupling section of the loaded stub-line, several conversion zeros are introduced at the same time. As the contribution of this work, multiple resonant modes and conversion zeros can be independently controlled by the corresponding parameters, enabling second-order single- and dual-band response with multi-mode high selectivity side-band and harmonic rejection characteristics out-of-band. With the detailed analysis of the surface current and field distributions, the polarization conversion mechanisms are revealed. Finally, the single-band and dual-band linear polarization converters are processed, and the measured and simulated results are in good agreement. As expected, the two polarization converters show excellent filtering features, which is beneficial for improving modulation accuracy and avoiding unwanted electromagnetic interference in various applications of multi-passband and multi-functional metasurfaces.