It is an urgent and significant issue to investigate the influence factors of functional devices and then improve, modify or control their performances, which has important significance for the practical application and electronic industry. Based on first principle and quantum transport calculations, the effects of compressive strain on the current transport and relative electrical properties (such as the electrostatic potential energy, built-in electric field, charge density and polarization, etc.) in gallium nitride (GaN) tunnel junctions are investigated. It is found that there are potential energy drop, built-in electric field and spontaneous polarization in the GaN barrier of the tunnel junction due to the non-centrosymmetric structure of GaN. Furthermore, results also show that all these electrical properties can be adjusted by compressive strain. With the increase of the applied in-plane compressive strain, the piezocharge density in the GaN barrier of the tunnel junction gradually increases. Accordingly, the potential energy drop throughout the GaN barrier gradually flattens and the built-in electric field decreases. Meanwhile, the average polarization of the barrier is weakened and even reversed. These strain-dependent evolutions of the electric properties also provide an atomic level insight into the microscopic piezoelectricity of the GaN tunnel junction. In addition, it is inspiring to see that the current transport as well as the tunneling resistance of the GaN tunnel junction can be well tuned by the compressive strain. When the applied compressive strain decreases, the tunneling current of the junction increases and the tunneling resistance decreases. This strain control ability on the tunnel junctions current and resistance becomes more powerful at large bias voltages. At a bias voltage of -1.0 V, the tunneling resistance can increase up to 4 times by a -5% compressive strain, which also reveals the intrinsic giant piezoelectric resistance effect in the GaN tunnel junction. This study exhibits the potential applications of GaN tunnel junctions in tunable electronic devices and also implies the promising prospect of strain engineering in the field of exploiting tunable devices.