The tunneling mechanisms of electron transfers (ETs) in photosynthetic reaction center of Blastochloris viridis are studied by the ab initio fragment molecular orbital (FMO) method combined with the generalized Mulliken-Hush (GMH) and the bridge Green function (GF) calculations of the electronic coupling TDA and the tunneling current method for the ET pathway analysis at the fragment-based resolution. For the ET from batctriopheophytin (HL) to menaquinone (MQ), a major tunneling current through Trp M250 and a minor back flow via Ala M215, Ala M216, and His M217 are quantified. For the ET from MQ to ubiquinone, the major tunneling pathway via the nonheme Fe2+ and His L190 is identified as well as minor pathway via His M217 and small back flows involving His L230, Glu M232, and His M264. At the given molecular structure from X-ray experiment, the spin state of the Fe2+ ion, its replacement by Zn2+, or its removal are found to affect the TDA value by factors within 2.2. The calculated TDA values, together with experimentally estimated values of the driving force and the reorganization energy, give the ET rates in reasonable agreement with experiments.