The molecular magnetic tunnel junction (MMTJ) with high tunnel magnetoresistance (TMR) is an important component for devices such as computers and electronic storage. With the rapid development of the modern electronics industry, the decrease of device size and the increase of area density, it is important to improve TMR technology. In addition, the computing process faces huge challenges. As the size of electronic devices decreases, small changes may cause completely different transmission characteristics, therefore the minute details of the device must be carefully controlled. In this paper, in order to find large TMR values and explore the role of symmetry on spin-polarized transport properties, γ-graphyne nanodots (γ-GYND) coupled between ferromagnetic (FM) metallic zigzag graphene nanoribbon (ZGNR) electrodes were used. Depending on the widths of the ZGNR and two types of contact positions between the ZGNR and γ-graphyne nanodots (γ-GYND), eight ZGNR/γ-GYND/ZGNR MMTJs with different symmetries were constructed. By using Keldysh non-equilibrium Green's function (NEGF) and density functional theory (DFT), the I-V curve, the spin-injection efficiency (SIE) and TMR of MMTJs were calculated. We found that the transport properties of these MMTJs differed substantially. For absolute symmetric MMTJs, due to the wave functions corresponding to the band structure near the Fermi energy having different parity, the electron transport between the wave functions with different parity is prohibited, so we can see that the spin-down current is always zero. This implies that these absolutely symmetrical structures have 100% spin injection efficiency over a wide range of bias voltages. In addition, the calculation results also show that these absolutely symmetric structures also have large TMR at low bias, up to 3.7 × 10 5 , indicating that these devices have a large magnetoresistance effect and high magnetic field sensitivity, which can be used in the read head of computer hard disks, MRAM, and various magnetic sensors. However, for these asymmetric MMTJs, since there is no limitation of the wave function parity of the left and right electrodes, the spin-up current and spin-down current fluctuated as the bias voltage increased, so perfect SIE does not appear. In addition, the calculation results showed that the TMR of asymmetric MMTJs were four orders of magnitude smaller than with symmetric MMTJs. Thus the symmetry of MMTJs has a great influence on the spin-polarized transport properties of the device. These absolutely symmetrical MMTJs have spin-polarized transport properties that are far superior to other MMTJs. This is conducive to the manufacture of spin filters, rectifiers, and various magnetic sensors. Finally, these excellent characteristics can be explained by the transmission coefficient, local density of states (LDOS) and band structure.