In this work, we propose a design in the proof-of-concept of a 1×3 two-mode selective silicon-photonics router/switch. The proposed device composes of a Y-junction coupler, two multimode interference (MMI) couplers, and two phase-shifters on the silicon-on-insulator (SOI) rib waveguides. The input modes of TE 0 and TE 1 can be arbitrarily and simultaneously routed to the yearning output ports by setting appropriate values (ON/OFF) for two tunable phase shifters (PSs). The structural optimization and efficient characterization processes are carried out by numerical simulation via three-dimensional beam propagation method. The proposed device exhibits the operation ability over the C-band with good optical performances in terms of insertion loss smaller than 1 dB, crosstalk under -19 dB, and relatively large geometry tolerances. Moreover, the proposed device can integrate into a footprint as compact as 5 µm × 475 µm. Such significant advantages are beneficial and promising potentials for very large-scale photonic integrated circuits, high-speed optical interconnects, and short-haul few-mode fiber communication systems.