Gauge-invariant string field theory is constructed for the closed string compactified on a torus in a generalized manner of Narain. On the basis of the observation that the coordinates of the compactified dimensions cannot be connected smoothly on the 3-string vertex, we show that it is necessary to multiply the vertex functional by the two-cocycle phase factor to achieve the gauge-invariance of the action. With this modified 3-string vertex used, all the identities concerning the *-product of string fields (e.g., Jacobi identity) are shown to hold in the same forms as in the ordinary non-compactified case.