A scroll expander has been designed to produce a shaft power from a R134a Rankine cycle for electricity generation. Heat was supplied to the Rankine cycle through a heat exchanger, which received heat from another cycle of water. In the water cycle, water was heated up in a boiler using biogenic solid fuel. The designed scroll expander was a horizontal type, and a trochoidal oil pump was employed for oil supply to bearings and Oldham-ring keys. For axial compliance, a back pressure chamber was created on the backside of the orbiting scroll base plate. Numerical study has been carried out to estimate the performance of the designed scroll expander. The expander was estimated to produce the shaft power of about 2.9 kW from a heat supply of 36 kW, when the temperature of R134a was $80^{circ}C$ and $35^{circ}C$ at the evaporator and condenser of the Rankine cycle, respectively. The expander efficiency was about 70.5%. When the amount of heat supply varied in the ranges of 7.5~55 kW, the expander efficiency changed in the range of 45.6~70.5%, showing a peak efficiency of 70.5% at the design shaft speed.