Ribbons made of anisotropic materials are ubiquitous in nature as well as in a variety of engineering systems, such as wood veneers, carbon fiber composites, liquid crystal displays (LCDs), and biological tissues like tendons and ligaments. Previous studies have showed that composite helices can exhibit diverse shapes, resulting from anisotropic driving forces and geometric misorientation between the principal axes of the driving forces and the geometric axes. Moreover, they exhibit interesting phenomenon such as multistability as we prescribe an appropriate initial curvature and the fiber orientation angle [1]. In this work, we derive a general nonlinear one-dimensional model for elastic ribbons that are made of composite laminates with thickness t, width a and length l, assuming t << a << l . We build upon previously developed model [2], by assuming isometric deformations, we consider the case of developable surfaces and treat their generatrixes as an internal variable. The equilibrium equations are derived from a variational approach, where the total strain energy is augmented with constraints that account for inextensibility and the fact that the ribbon may contain a non-zero geodesic curvature. As an example, we investigate a thin fiber reinforced composite laminate with a prescribed initial curvature under thermal residual stresses. We further examine the stability of such ribbons, adapting classical methods for rods. The results are compared with a corresponding finite element model discretized with 2D shell elements. Through a parametric study, we show how the resultant principal curvatures and chirality can be further tuned using curved composite ribbons. This work can advance research on the programmable design of ribbon-type structures, such as helices, particularly relevant in deployable and morphing structures.