As a building material, engineered bamboo has caught attention around the world due to its advantages in energy conservation and environmental protection. The seismic performance of bamboo buildings needs to be evaluated to further promote the use of bamboo materials in building construction. We studied the seismic response of a 3-story bamboo frame structure numerically using nonlinear dynamic time history analysis. A simplified modeling method for bamboo column-beam joints was proposed in the numerical model. The hysteresis behaviour of the joint was simulated by Pinching 4 material in OpenSEES, with the parameters calibrated through test results. Comparative analysis shows that the proposed modeling method could reasonably reflect the pinching effect and the degradation of the joint hysteretic behavior. A total of 20 ground motions with three intensities were involved in the nonlinear dynamic analysis. The results demonstrate that the frame meets target performance levels, providing evidence for the further popularization of engineered bamboo structures.