In the present paper, the effect of parameterization on the results of isogeometric analysis of free-form approximated curved beams is investigated. An Euler–Bernoulli beam element for an initially curved beam with variable curvature is developed. The model is applied to four different examples. The effect of three parameterization strategies (the equally spaced method, the chord length method and the centripetal method) in the curve approximation process is considered. Also, the effect of least square approximation error is taken into consideration. The results strongly suggest avoiding the equally spaced method. Among the chord length and centripetal methods, the method which leads to a less least square error is recommended.