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In this paper, we have investigated a spatial predator-prey system with hunting cooperation in predators and type-I functional response. Using linear stability analysis, we obtain the stipulations for diffusive instability and identify the corresponding domain in the space of control parameters. Using qualitative and quantitative analysis, we obtain complex patterns, namely, spotted pattern, stripe pattern and mixed pattern in the Turing domain, by varying the rate of hunting cooperation in predators and diffusion coefficients of prey and predators. The results focus on the effect of hunting cooperation in pattern dynamics of a diffusive predator-prey model and help us in better understanding of the dynamics of the predator-prey interaction in real environment.