This article proposes a unified design method for a highly efficient wideband transmissive linear-to-circular polarization converter composed of two orthogonal adjacent-order bandpass filtering elements for the first time. First, the linear-to-circular polarization converter is constructed to convert two orthogonal linearly polarized (LP) spatial waves split from a 45°-slant incident plane wave into a desired circularly polarized (CP) wave. Taking advantage of the wideband filter synthesis method and phase shifter theory, polarization converter elements with prescribed specifications [e.g., fractional bandwidth (FBW) and Chebyshev passband ripple] are then synthesized by the corresponding low-characteristic-impedance bandpass filtering networks with the loading of shunt short-circuited stubs on quarter-wavelength transmission line (TL) sections. The adjacent-order phase difference function with a natural ±90° value at a center frequency can be simultaneously manipulated by a filtering bandwidth. The theoretical axial ratio (AR) curve is calculated by the synthesized magnitude responses and phase deviation (PD) function. The design guideline is then summarized. Finally, based on the third- and fourth-order bandpass filtering networks, a prototype of the proposed linear-to-circular polarization converter operating at 5 GHz with a designable 70% 3 dB AR bandwidth is implemented, fabricated, and tested by the free-space measurement method. The transmitted CP wave with three in-band AR minima and relatively stable angular performances can be efficiently converted from the incident LP spatial wave as well verified in the experiment. The AR curves and design requirements of different adjacent-order bandpass filtering combinations are further explored according to the proposed design guideline.