We propose a novel mode multiplexer based on phase plates followed by a Mach-Zehnder interferometer (MZI) with image inversion. After the higher-order modes are selectively converted from fundamental linear-polarized (LP) modes by the phase plates, the converted modes are coupled without fundamental loss using MZI with image inversion, in which the original spatial pattern and inverted pattern of the optical signal are interfered. Our scheme is also applicable to the coupling of degenerated LP modes such as LP(11a) and LP(11b). First, we numerically and experimentally evaluate the performance of the mode converter based on phase plates. The mode converter is suitable as long as the five LP modes such as LP(01), LP(11ab) and LP(21ab) are sustained in a few-mode fiber (FMF), although the crosstalk due to excitation of undesirable modes is unavoidable when the higher-order modes over LP(02) are sustained in FMF. Next, we develop and characterize the proposed mode multiplexers based on phase plates and MZIs with image inversion. The insertion loss is suppressed to around 3 dB for mode multiplexing of LP(11a) and LP(11b). Using a fabricated mode multiplexer for LP(31a) and LP(31b), we measure the bit-error rate performance of single-polarization mode-multiplexed quadrature-phase shift keying optical signals.