The crystal plasticity finite element modeling (CPFEM) is realized in commercial finite element code ABAQUS with UMAT subroutine on the basis of the crystal plasticity theory of rate dependent polycrystal constitutive relations in the mesoscopic scale. The initial orientations obtained by electron backscatter diffraction (EBSD) are directly input into the CPFEM to simulate the mechanical response of polycrystalline 1050 pure Al in uniaxial tensile deformation. Two polycrystal models and two tensile strain rates were used in the simulations. The stress-strain curves of tensile deformation were analyzed. The predictions and the corresponding experiment result show reasonable agreement and slight deviation with experiments. The flow true stress of strain rate 0.01 s^-1 is higher than that of strain rate 0.001 s^-1. At the strain less than 0.05, the stress saturated rate of the experiment is higher than the simulated results. However, the stress saturated rate of the experiment becomes gentler than the corresponding simulated predictions at the strain over 0.05. Also, necking was simulated by the two models, but the necking strain is not well predicted. Tensile textures at strain 0.25 were predicted at the low strain rate of 0.001 s^-1. The predictions are in good accord with the experimental results.