This paper presents a tri-uniform bond stress model for predicting the lap splice strength of reinforcing bar at the critical bond splitting failure. The proposed bond distribution model consists of three zones, namely, splitting zone, post-splitting zone and yielding zone. In each zone, the bond stress is assumed to be constant. The models for bond strength in each zone are adopted from previous studies. Combining the equilibrium, strain-slip relation and the bond strength model in each zone, the steel stress-slip model can be derived, which can be used in the nonlinear frame analysis of the column. The proposed model is applied to derive explicit equations for predicting the strength of the lap splice strengthened by fiber reinforced polymer (FRP) in both elastic and post-yield ranges. For design purpose, a procedure to calculate the required FRP thickness and the number of FRP sheets is also presented. A parametric investigation was conducted to study the relation between lap splice strength and lap splice length, number and thickness of FRP sheets and the ratio of concrete cover to bar diameter. The study shows that the lap splice strength can be enhanced by increasing one of these parameters: lap splice length, number or thickness of FRP sheets and concrete cover to bar diameter ratio. Verification of the model has been conducted using experimental data available in literature.