We synthesize a new titanium-oxide compound AlTi2O5 with pseudobrookite-type structure. The formal valence of Ti is 3.5+ that is the same as the Magnéli compound Ti4O7 and the spinel compound LiTi2O4. AlTi2O5 exhibits insulating behavior in resistivity. Using experimentally determined crystal structure, we perform the first-principles calculations for the electronic structures. Experimentally suggested random distribution of Al and Ti is not the origin of the insulating behavior. The Fermi surfaces for nonrandom AlTi2O5 show cylindrical shapes reflecting a layered structure, which indicates a possible nesting-driven order. Constructing a tight-binding model from the first-principles calculations, we calculate the spin and charge susceptibilities using the random phase approximation. We suggest possible charge-density-wave state forming Ti3+ chains separated from each other by Ti4+ chains, similar to the low-temperature phase of Ti4O7.