A non-spinning projectile that is self-guided to a laser designated target and is configured to be fired from a small caliber smooth bore gun barrel has an optical sensor mounted in the nose of the projectile, a counterbalancing mass portion near the fore end of the projectile and a hollow tapered body mounted aft of the counterbalancing mass. Stabilizing strakes are mounted to and extend outward from the tapered body with control fins located at the aft end of the strakes. Guidance and control electronics and electromagnetic actuators for operating the control fins are located within the tapered body section. Output from the optical sensor is processed by the guidance and control electronics to produce command signals for the electromagnetic actuators. A guidance control algorithm incorporating non-proportional, "bang-bang" control is used to steer the projectile to the target.