We study a new variant of the bin packing problem. Given a set of items, each item has a set of colors. Each bin has a color capacity, the total number of colors for a bin is the union of colors for its items and can not exceed the bin capacity. We want to pack all items into the minimal number of bins. For this NP-hard problem we apply the column generation technique based on the VNS matheuristic for the pricing problem. To get optimal or near optimal solutions we apply VNS matheuristic again using optimal solution for the large scale linear programming relaxation. Computational experiments are reported for the randomly generated test instances with large bin capacity and number of items up to 250.