For speeding up the complex fractured reservoir simulating, we have given more attention to reducing runtime and improving efficiency of the solver. In this work, we describe an improved and computationally efficient version of Newton's method, which reduces the non-linear iteration count, increases time steps, and furthermore reduces time spent in nonlinear loops of reservoir simulating. Safeguarded variants of Newton's method which have used in current reservoir simulators cannot guarantee convergence of the solution, especially in highly heterogeneous, detailed and fractured reservoirs. In such simulators time step chopping is often observed. From other hand, with growing complexity, convergence difficulties can lead to considerable losses in computational effort and prohibitively small time steps. For overcoming this problem, an improved and computationally efficient version of Newton's method, which uses higher order terms in the Jacobian matrix in addition to the Newton's basic linear terms to account for cross variable dependencies including a high-tech stable linear solver, is proposed. This scheme leads to a smaller number of non-linear iterations compared to other known commercial simulators with larger time steps. In addition to SPE10 model, an under saturated fractured black-oil reservoir model, including single and dual grid blocks together, with dimension of 124*105*60 grid blocks is used to evaluate the method efficiency, by comparing the results using the known commercial simulator. This heterogeneous model includes the features of hysteresis, gravity drainage, oil-gas surface tension, and moderate aquifer with 8 active production wells which have produced for 24 years. The numbers of time steps are 525 and 2693 for proposed method and the commercial simulator, respectively. The numbers of Newton iterations are 1667 and 9399, and the average time step size is 26.2 and 5.62 days, for proposed method and the commercial simulator, respectively. These results obviously indicate the efficiency of the proposed method in reducing Newton's iterations and accordingly increasing simulation speed. The novelty of the proposed creative method is in reducing non-linear Newton's iterations and increasing time steps which leads to reduced simulating elapsed time, which has never been observed in current simulators.