The orientation of part in the additive manufacturing process is one of the most important factors should be considered in the additive manufacturing process. In the additive manufacturing process, the part orientation factor can significantly affect the part properties such as the surface roughness, strength, the manufacturing time and amount of support materials. The manufacturing time is a key factor that can influence the total production cost. Therefore, to minimize the manufacturing time, the optimum orientation of parts should be determined. In this paper, a new method is introduced to estimate the built time of the parts through the additive manufacturing process. According to the proposed method, a practical equation is extracted to estimate the built time of the parts with related to the number of layers and amount of the support materials. The method is capable to estimate the built time of a part associated to the part orientations. The efficiency of the proposed method is demonstrated through a case study in two different type of orientation, and the computational results are compared with the obtained results from the simulations in MankatiUM V5.3 and Repetier-Host software. The average of proposed method relative error in the first type of orientation in comparison with MankatiUM and Repetier-Host software results are, respectively, 5 and 10 percent and for the second type of orientation are 7 and 8 percent. Moreover, calculation cost of proposed method is 140 and 100 times faster than MankatiUM and Repetier-Host software, respectively.