The success of the lattice Boltzmann method requires efficient parallel programming and computing power. Here, we present a new lattice Boltzmann solver implemented in Taichi programming language, named Taichi-LBM3D. It can be employed on cross-platform shared-memory many-core CPUs or massively parallel GPUs (OpenGL and CUDA). Taichi-LBM3D includes the single- and two-phase porous medium flow simulation with a D3Q19 lattice model, Multi-Relaxation-Time (MRT) collision scheme and sparse data storage. It is open source, intuitive to understand, and easily extensible for scientists and researchers.