We present an integral-based technique (IBT) algorithm to accelerate supernova (SN) radiative transfer calculations. The algorithm utilizes “integral packets,” which are calculated by the path integral of the Monte Carlo energy packets, to synthesize the observed spectropolarimetric signal at a given viewing direction in a 3-D time-dependent radiative transfer program. Compared to the event-based technique (EBT) proposed by Bulla et al. (Mon Not R Astron Soc 450:967–981;2015) our algorithm significantly reduces the computation time and increases the Monte Carlo signal-to-noise ratio. Using a 1-D spherical symmetric type Ia supernova (SN Ia) ejecta model DDC10 and its derived 3-D model, the IBT algorithm has successfully passed the verification of spherical symmetry and cross comparison on a 3-D SN model with direct counting technique (DCT) and EBT. Notably, with our algorithm implemented in the 3-D Monte Carlo radiative transfer code SEDONA, the computation time is faster than EBT by a factor of \(10{-}30\) , and the signal-to-noise (S/N) ratio is better by a factor of \(1.5{-}3\) , with the same number of Monte Carlo quanta.