In this paper, we define a new kind of curve called N-slant curve whose principal normal vector field makes a constant angle with the Reeb vector field ξ in Sasakian 3-manifolds. Then, we give some characterizations of N-slant curves in Sasakian 3-manifolds and we obtain some properties of the curves in R3(−3) . Moreover, we investigate the conditions of C−parallel and C−proper mean curvature vector fields along N-slant curves in Sasakian 3-manifolds. Finally, we study N-slant curves of type AW(k).