  We study one-photon transitions between heavy baryon states in the framework of a relativistic three-quark model. We calculate the one-photon transition rates for ground-state to ground-state transitions and for some specific excited state to ground-state transitions. Our rate predictions for the most important transitions are: $\Gamma(\Sigma^{+}_{c}\to \Lambda_c^+\gamma)= 60.7\pm 1.5 $ KeV, $\Gamma(\Xi^{'+}_{c}\to \Xi_c^+\gamma) = 12.7\pm 1.5$ KeV, $\Gamma(\Lambda_{c1}(2593)\to\Lambda_c^+\gamma)=104.3\pm 1.3$ KeV. 
One-Photon Transitions between Heavy Baryons in a Relativistic   Three-Quark Model