We analyze a random process in a random media modeling the motion of DNA nanomechanical walking devices. We consider a molecular spider restricted to a well-defined one-dimensional track and study its asymptotic behavior in an i. i. d. random environment. The spider walk is a continuous time motion of a finite ensemble of particles on the integer lattice with the jump rates determined by the environment. The particles mutual location must belong to a given finite set of configurations L, and the motion can be alternatively described as a random walk on the ladder graph Z × L in a stationary and ergodic environment. Our main result is an annealed central limit theorem for this process. We believe that the conditions of the theorem are close to necessary.