A suppressor adapter attachable to firearms of various sizes and shapes. The adapter includes an anchor securable to a smooth section of a barrel, preferably proximally with respect to any obstructions located near the muzzle end of the barrel, and a housing configured to engage the anchor. The housing has a size and/or shape that reaches over and/or around various obstructions, protrusions and geometries near the muzzle end of the barrel. The device further includes an alignment surface intended to receive the muzzle of the firearm and guide the muzzle into longitudinal and concentric alignment with a suppressor secured to a distal end of the housing.