Phonon Monte Carlo method is a popular method for modeling particle dominated phonon transport. Its accuracy critically depends on its inputs such as relaxation time and dispersion, which are difficult to be obtained accurately and efficiently. As a result, empirical models with many fitting parameters are often used. In addition, for large-scale 3D nanostructured systems, the required computational cost is very high. In this article, we present an efficient and highly parallelizable phonon Monte Carlo method using MFP-cumulative thermal conductivity as the only input. The efficiency is enhanced by incorporating the recently proposed variance-reduction method, and the accuracy is ensured because the MFP-based cumulative thermal conductivity can be accurately obtained by experiments or first principles calculation. Moreover, with the MEP-cumulative thermal conductivity as the input, optical phonons can be naturally included in the calculation, which further improves the accuracy.