In the field of molecular electronics, structural design of a molecule is necessary to achieve different functionalities. The rectification behaviour of single-molecule diodes is one of the most attractive device features. The electron transport of symmetric and asymmetric single molecular junctions was studied, which correspond to tetraphenyl and dipyrimidiny-diphenyl monomolecular junctions, respectively. Both of them were covalently bonded to two gold electrodes. Asymmetric diblock molecules exhibited significant rectifying behaviour compared to their homologous symmetric blocks, and the electrons flow from diphenyl to dipyrimidinyl. The first-principles method was used, including density functional theory (DFT) and the non-equilibrium Green's function (NEGF) method, to study the electronic structure and quantum transport of single-molecule junctions. The asymmetry in the $I$-$V$ could be explained by the localisation of the electron density at one end of the asymmetric molecule, leading to a nonequilibrium effect under bias voltage. Theoretical results agreed qualitatively with the experimental works reported in the literature. Moreover, upon investigating different contacting ends, it was found that the scanning tunneling microscope (STM)-tip setup in the experiment would cancel the rectification effect to some extent; meanwhile, the STM-tip results also confirmed the previous theoretical prediction.