After numerous theoretical and experimental researches to identify the properties of graphene, in recent years it is found that phosphorene has also a very good potential for electronic applications. Phosphorene has a honeycomb lattice structure from single-layer black phosphorus which has been produced this material in laboratories. Phosphorene has a finite band gap and compared with other materials has a high mobility. Thus it has extensive applications in nano-electronics, thermos-electronics and opto-electronics. To study phase transition from insulator to metal, in this thesis we change hopping parameter in tight-binding phosphorene Hamiltonian. The change in hopping parameters is as a consequence of application of pressure or stress to lattice; this procedure would change lattice constant. By changing the lattice constant hopping probability will also change. When the unidimensional pressure along X axis reaches to a definite value that horizontal lattice constant decreases by 15 percent, the coefficient of second hopping probability will fall from to As a result energy gap of phosphorene changes from 1.8 eV to zero. Due to the puckered and special lattice of phosphorene metal-insulator transition at finite temperature can be examined in this material. For this purpose Hubbard model which is a many body model in condensed matter physics, is used. Since Hubbard model in two dimensions can not be solved easily, it is expected that this model will not have precise results for studying metal-insulator phase transition in phosphorene. Another approximation to get precise results is dynamic mean-field theory, which considers the effect of crystal lattice as a mean-field in a site (bath). In dynamic mean-field theory, bath parameters (energy and hopping) and Weiss function are used to describe mean-field instead of all sites. For this purpose to solve eigenvalue problem a diagonalization algorithm is used. In this research Lanczos method is used, from which desired states from Anderson impurity Hamiltonian can be obtained. In this step because Weiss function and the impurity Green function have been obtained, system self-energy can be calculated from Dyson equation. By using Dyson equation and Weiss function for the second time new bath coefficients are calculated. Finally this cycle continues until impurity Green function and lattice Green function converge. In Lanczos algorithm large and sparse Hamiltonian become a three-diagonal with smaller order. Ground state can be calculated with this algorithm. This algorithm with the use of a guessed vector and multiplying Hamiltonian matrix by this vector calculates the three-diagonal matrix components. The convergence condition in this algorithm is that the difference minimum energies between two iteration should be lower than a given small value (e.g. ).