The methods used in practice for realigning railway horizontal curves are based on trial and error. In this paper, a linear-integer optimization model that minimizes the absolute deviations between the realigned curve and an ideal curve is developed. The model includes constraints related to (1) the maximum allowable shifts of the railway track, (2) coincidence of the realigned and original tangents, and (3) equality of the central angles of the realigned and ideal curves. The model is extended to accommodate situations of spiralling an old curve (not originally spiralled) during realignment. Other realignment objectives such as minimization of the total track shifts and minimization of the maximum deviation are presented. The output of the model includes the required track shifts to realign the existing curve to a smoother curve. Application of the model is illustrated using real-world examples. This model, which is readily solved by existing computer software, should be valuable for railway engineers who are concerned with the safety and smooth-ride of railways.