With the development of pulse amplification and compression technology, the peak power of the pulse has been improved by several orders of magnitude, and it is possible for the ultra strong laser field to affect nuclei directly. The α decay, as one of the most major forms in nuclear reaction, is a critical research topic in nuclear physics. According to the theory of Gamow model explaining nuclear α decay in quantum mechanics, double folding model solving nuclear potential energy, and cluster model describing atomic nucleus, we present a complete set of solutions for the half-life of nuclear α decay to study the influence of ultra strong laser field on nuclear α decay. These half-lives of α decay of different nuclei from medium to heavy in the absence of laser field are obtained, which accord well with the experimental data. Subsequently, we introduce the effects of ultra strong laser field into our theoretical method to achieve the variations of the half-life of nuclear α decay. Considering that the optical period of the laser pulse is much longer than the theoretical tunneling time and the Lorentz force is much smaller than the Coulomb force, the laser field is treated as an electrostatic field. The results show that the half-life of nuclear α decay will reduce about 0.1% by the strong laser field with a peak power density of about 1.0×10²⁶ W/cm², demonstrating that the half-life of nuclear α decay is effectively affected by the strong laser field. Furthermore, the influences of the nuclear parameters, e.g. total quantum number G describing α particle orbits, and α decay reaction energy Q_α, on the variations of these half-lives of α decay of different nuclei are discussed with the help of the calculation results. The dependence of the half-lives of nuclear α decay on the laser peak power density is also explained correspondingly. In summary, we provide a more accurate method of calculating the half-life of nuclear α decay, which is used to study the influences of ultra strong laser field on these half-lives of nuclear α decay of different nuclei. With the further construction of strong laser devices, more interesting phenomena and results will be found from the experiment on the atomic nucleus under strong laser field.