We study the role of the dimer structure of light-harvesting complex II (LH2) in excitation transfer from the LH2 [without a reaction center (RC)] to the LH1 (surrounding the RC) or from the LH2 to another LH2. The excited and unexcited states of a bacteriochlorophyll (BChl) are modeled by a quasispin. In the framework of quantum open system theory, we represent the excitation transfer as the total leakage of the LH2 system and then calculate the transfer efficiency and average transfer time. For different initial states with various quantum superposition properties, we study how the dimerization of the B850 BChl ring can enhance the transfer efficiency and shorten the average transfer time.