To improve the performance of optical computed tomography (OpCT) reconstruction in the case of limited projection views, maximum entropy (ME) algorithms were proposed and can achieve better results than traditional ones. However, in the discrete iterative process of ME, the variables of the iterative function are continuous. Hence, interpolation methods ought to be used to improve the precision of the iterative function values. Here, a sinc function interpolation approach was adopted in ME algorithm (SINCME) and its reconstruction results for OpCT with limited views were studied using four typical phantoms. Compared results with ME without interpolation, traditional medical CT back-projection algorithm (BP), and iterative algorithm algebraic reconstruction technique (ART) showed that the SINCME algorithm achieved the best reconstruction results. In an experiment of emission spectral tomography reconstruction, SINCME was also adopted to calculate the three-dimensional distribution of physical parameters of a candle flame. The studies of both algorithm and experiment demonstrated that SINCME met the demand of limited-view OpCT reconstruction.