Based on an effective single cluster growth algorithm, bond percolation on square lattice with the nearest neighbors, the next nearest neighbors, up to the 5th nearest neighbors are investigated by Monte Carlo simulations. The bond percolation thresholds for more than 20 lattices are deduced, and the correlations between percolation threshold $p_{\rm c}$ and lattice structures are discussed in depth. By introducing the index $\xi = \displaystyle\sum\nolimits_{i} z_{i} r_{i}^{2} / i$ to remove the degeneracy, it is found that the thresholds follow a power law $p_{\rm c} \propto \xi^{-\gamma}$ , with $\gamma \approx 1$ , where $z_{i}$ is the ith neighborhood coordination number, and $r_{i}$ is the distance between sites in the i-th coordination zone and the central site.