Z-curve’s encoding and decoding algorithms are primely important in many Z-curve-based applications. The bit interleaving algorithm is the current state-of-the-art algorithm for encoding and decoding Z-curve. Although simple, its efficiency is hindered by the step-by-step coordinate shifting and bitwise operations. To tackle this problem, we first propose the efficient encoding algorithm LTFe and the corresponding decoding algorithm LTFd, which adopt two optimization methods to boost the algorithm’s efficiency: 1) we design efficient lookup tables (LT) that convert encoding and decoding operations into table-lookup operations; 2) we design a bit detection mechanism that skips partial order of a coordinate or a Z-value with consecutive 0s in the front, avoiding unnecessary iterative computations. We propose order-parallel and point-parallel OpenMP-based algorithms to exploit the modern multi-core hardware. Experimental results on discrete, skewed, and real datasets indicate that our point-parallel algorithms can be up to 12.6× faster than the existing algorithms.