This letter investigates an iterative algorithm for decoding analog error-correcting codes. First, the shift-map code, one of the widely studied analog codes, is generalized to yield a new family of codes with a more flexible tradeoff between errors at low and high signal-to-noise ratios. Then, an iterative decoding algorithm for the generalized shift-map codes is derived from a message-passing process on a sparse factor graph. Numerical simulations demonstrate that the proposed algorithm decodes generalized shift-map codes following a small number of iterations. Combined with the efficient decoding algorithm, the flexibility of the generalized shift-map codes will enhance the applicability of analog error-correcting codes.