Non-orthogonal multiple access (NOMA)-based cognitive wireless networks can improve the spectral efficiency to utilize the vacant spectrum resource and exploit the power domain diversity. In this paper, we formulate a max-min resource allocation problem for video traffic in NOMA-based cognitive wireless networks as a mixed integer non-linear programming (MINLP) problem. The max-min video transmission problem is subject to the constraints of maximum accessed user number at each subchannel, total available energy of each secondary user, video encoding characteristics, and interference power threshold. To solve the formulated MINLP problem, we divide it into two subproblems, i.e., a power allocation and secondary user scheduling subproblem, and a video packet scheduling subproblem. First, we apply a successive convex approximation to transform the joint power allocation and secondary user scheduling subproblem into a bi-convex programming problem. Second, the binary search and dual decomposition methods are combined to obtain the approximated optimal power allocation and secondary user scheduling solutions. Finally, we propose a heuristic packet scheduling algorithm. Simulation numerical results show that the proposed algorithm improves the video quality and guarantees the fairness among different secondary users.