The behavior of an elastic chain of coupled self-propelled particles in a two-dimensional potential with Gaussian colored noise is investigated. The channel and colored noise regulates the directed transport of the system. The chain of particles changes the moving direction with increasing modulation constant of potential. The average velocity of the chain shows periodic fluctuation with increasing phase shift of the potential. Strong coupling between particles inhibits the directed transport speed of the system. Large translation noise intensity is good for the directed transport in the - or , but large self-correlation time inhibits this phenomenon. The effect of the self-propulsion speed is influenced by the modulation parameter of the potential. The elastic chain moves in the when the angle noise intensity is zero. Noise intensity and self-correlation time of the angle noise have a complicated effect on the system.