Do I need a box spring with this hybrid mattress?

No box spring is required. This is a 13.5-inch hybrid with its own 1000-coil support core, so it needs a firm, even foundation, not a traditional bouncy box spring. A platform bed, slatted frame with gaps under about 3 inches, an adjustable base, or a solid foundation all work. A sagging or wide-slat base is the main thing to avoid, since it can undermine the coil support and affect warranty coverage.