The simulation and optimization of a hybrid photovoltaic/biomass stand-alone system for a residential building in Makurdi was carried out using HOMER software model 2.81. The lifetime of the project is 25 years and a real interest rate of 6% per annum was assumed. The average hourly electrical load demand/consumption data for a three bedroom residential building in Makurdi was measured for a week using digital Owl metre model CM199 and the values inputted into HOMER in order to simulate the power consumption for a twelve month (12) period. The solar resource data with an annual average insolation of 4.48kWh/m2/d for Makurdi location was obtained from the NASA Langley Research Centre website in order to calculate daily radiation and monthly average values of clearness index. The sizes of the different components were determined to make sure their sizes suit the load demand. The optimal system obtained from the simulation is the configuration consisting of 2kW PV array, 1kW biomass generator, 1kW converter and 12 LP16trojan. Its NPC is $20,184 with initial capital requirement of $8,990, annual operation cost of $873. The system has a yearly excess electricity of 3.36 kWh/yr (0.074%) and unmet load of 0.256 kWh/yr (0.0063%). The results obtained show that the PV/biomass hybrid system is technically and economically feasible for the location of choice.