Crude oil is an important feedstock for the petrochemical industry and the dominant energy source driving the world economy, but known oil reserves will cover demand for no more than 50 years at the current rate of consumption. This situation calls for more efficient strategies for converting crude oil into fuel and petrochemical products. At present, more than 40% of oil conversion is achieved using catalysts based on faujasite; this zeolite requires extensive post-synthesis treatment to produce an ultrastable form, and has a large cavity accessible through four 0.74-nm-wide windows and thus limits the access of oil molecules to the catalytically active sites. The use of zeolites with better accessibility to their active sites should result in improved catalyst efficiency. To date, two zeolites with effective pore diameters exceeding that of faujasite have been reported, but their one-dimensional pore topology excludes use in oil refining. Similarly, zeolites with large pores and a three-dimensional pore topology have been reported, but in all these materials the pore openings are smaller than in faujasite. Here we report the synthesis of ITQ-21, a zeolite with a three-dimensional pore network containing 1.18-nm-wide cavities, each of which is accessible through six circular and 0.74-nm-wide windows. As expected for a zeolite with this structure, ITQ-21 exhibits high catalytic activity and selectivity for valuable products in preliminary oil refining tests.