Serial concatenation of Hamming codes and an accumulator has been shown to achieve near capacity performance at high code rates. However, these codes usually exhibit poor error floor performance due to their small minimum distances. To overcome this weakness, we propose to replace the outer Hamming codes by product codes constructed from Hamming codes and single-parity-check codes. In this way, the minimum distance of the outer code can be doubled, which is expected to increase the minimum distance of the serially concatenated code and thus to improve error floor performance. Three-dimensional EXIT chart is used for their convergence analysis and the derived thresholds are shown to be close to Shannon limit. Low weight distance spectrum of the proposed code is also calculated and compared with the original code. Simulation results show that the proposed codes can lower the error floor by two orders of magnitudes without waterfall performance degradation at short block length.