The model of relativistic particle with rigidity whose action A=−α∫ kds depends on the curvature of particle world trajectory k, is studied. The classical motion of the particle is shown to go along a helical line at superrelativistic velocity and its translational motion along the momentum direction—at the velocity of light (c). After quantization, the parameter a becomes integer, α=n, n>0. The quantum states of the system are massless states of helicities λ=n and λ=−n in which the evolution of gauge-invariant coordinate occurs at velocity c.