A four-mode (de-)multiplexer with transverse electric field light (TE0-TE3) is experimentally demonstrated on a thin film lithium niobate-silicon rich nitride hybrid platform. Enabled by cascaded asymmetrical directional couplers, a (de-)multiplexer with low insertion loss (0.38 dB to 1.6 dB) and low cross talk (-18.46dB to -20.43dB) is obtained at 1550 nm. All channels have cross talk <-16dB from 1480 nm to 1580 nm. The transmission of 4×50 Gbps on-off keying signals is experimentally achieved on the proposed (de-)multiplexer. Experimental results show that the proposed (de-)multiplexer is a promising approach to enhance the transmission capacity in thin film lithium niobate based photonics integrated circuits.