A tubular lock unit has a lock and key. An upper pin seat and a lower pin seat with multiple pins are respectively mounted in the lock. A shaft is inserted into the lower pin seat and connected to the upper pin seat. The upper pin seat has an annular keyway and a slot is defined in a sidewall. The key has a barrel and a protrusion extending out of the barrel. When the key is inserted into the keyway, the protrusion is inserted into the slot and a lower end of the protrusion meets with an upper end of the lower pin seat to rotate the upper pin seat. When an improper key is inserted into the keyway and rotated, at least one of the pins will remain extended into the upper pin seat to prevent rotation.