Capacitive energy storage is distinguished from other types of electrochemical energy storage by short charging times and the ability to deliver significantly more power than batteries. A key limitation to this technology is its low energy density and for this reason there is considerable interest in exploring pseudocapacitive materials where faradaic mechanisms offer increased levels of energy storage. Here we show that the capacitive charge-storage properties of mesoporous films of iso-oriented alpha-MoO3 are superior to those of either mesoporous amorphous material or non-porous crystalline MoO3. Whereas both crystalline and amorphous mesoporous materials show redox pseudocapacitance, the iso-oriented layered crystalline domains enable lithium ions to be inserted into the van der Waals gaps of the alpha-MoO3. We propose that this extra contribution arises from an intercalation pseudocapacitance, which occurs on the same timescale as redox pseudocapacitance. The result is increased charge-storage capacity without compromising charge/discharge kinetics in mesoporous crystalline MoO3.