We consider a two-degree-of-freedom block-spring model, in which two blocks (Block 1 and Block 2) are connected by a spring and driven by a slowly moving driver. Assuming a rate- and state-dependent friction law, we set the friction parameters such that dynamic instability occurs at Block 1. Episodic aseismic slip occurs at Block 2 when its frictional parameters are near the stability transition. When the stress has accumulated to approximately a steady state level during an interseismic period, Block 2 starts a slow slip. Quasi-static oscillation in the stress and slip velocity occurs with decaying fluctuation amplitudes leading to the steady state values. The decaying oscillation could be a plausible generation mechanism of the episodic aseismic slip observed in the Tokai district, Japan, since 2001. We also consider various slip modes on a plate boundary based on this two-block model associated with the interaction between different frictional properties.