The tetragonal hollandite structure (KAlSi3O8 hollandite) has been studied up to 32 GPa at room temperature using high-pressure in-situ X-ray diffraction techniques. A phase transformation from tetragonal I4/m phase to a new phase was found to occur at about 20 GPa. This transition is reversible on release of pressure without noticeable hysteresis and hence this new high-pressure phase is unquenchable to ambient conditions. The volume change associated with the transition is found to be small (not measurable), suggesting a second order transition. The diffraction pattern of the high-pressure phase can be indexed in a monoclinic unit cell (space group I2/m), which is isostructual with BaMn8O16 hollandite. The γ angle of the monoclinic unit cell increases continuously above the transition. A Birch-Murnaghan equation of state fit to pressure-volume data obtained for KAlSi3O8 hollandite yields a bulk modulus K0 = 201.4 (7) GPa with K′0 = 4.0.