In the present paper we have studied the propagation of optical beams in a circularly curved graded-index fibre. A closed-form expression for the kernel has been obtained, from which one can determine the field distribution at any point inside the fibre. For the special case of a Gaussian beam incident on the face of a fibre, an analytic expression for the intensity distribution has been obtained from which one can easily determine the path of the centre of the beam. Several incident conditions have been considered and it is shown that the beam, in general, follows a skew path, though there are specific cases when it stays in the meridional plane only. In practical cases the ellipticity introduced due to the bending of the fibre, is very small.