Weakly coupled-mode division multiplexing (MDM) over few-mode fibers (FMF) for short-reach transmission has attracted great interest, which can avoid multiple-input-multiple-output digital signal processing (MIMO-DSP) by greatly suppressing modal crosstalk. In this paper, step-index FMF supporting 4 linearity polarization (LP) modes for MIMO-free transmission is designed and fabricated for the first time, to our knowledge. Modal crosstalk of the fiber is suppressed by increasing the mode effective refractive index differences. The same fabrication method as standard single-mode fiber is adopted so that it is practical and cost-effective. The mode multiplexer/demultiplexer (MUX/DEMUX) consists of cascaded mode-selective couplers (MSCs), which are designed and fabricated by tapering the proposed FMF with single-mode fiber (SMF). The mode MUX and DEMUX achieve very low modal crosstalk not only for the multiplexing/demultiplexing but also for the coupling to/from the FMF. Based on the fabricated FMF and mode MUX/DEMUX, we successfully demonstrate the first simultaneous 4-modes (LP01, LP11, LP21 & LP31) 10-km FMF transmission with 10-Gb/s intensity modulation and MIMO-free direct detection (IM/DD). The modal crosstalk of the whole transmission link is successfully suppressed to less than -16.5 dB. The experimental results indicate that FMF with simple step-index structure supporting 4 weakly-coupled modes is feasible.