The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state is systematically examined in a generic model of quasi-one-dimensional (Q1D) type-II superconductors that has six hopping integrals of electrons as model parameters. For a magnetic field parallel to the conductive layers, the upper critical field H c2 is strongly enhanced by the FFLO state at low temperatures and sensitively depends on the angle ϕ between the in-plane magnetic field and the highly conductive chain (the crystal a -axis). As a result, H c2 exhibits sharp peaks at the optimal angles ϕ = ± ϕ 0. Since the optimal angle ϕ 0 strongly depends on the structure of the Fermi surface, we examine their correlation, searching for an intuitive method to find ϕ 0 from the shape of the... Fermi surface. For this purpose, we define quantities that quantify the warp of each sheet ( kx > 0 or kx < 0) of the Q1D open Fermi surface and the shear distortion between the two sheets. We estimate the optimal angles for numbers of the parameter sets chosen systematically from a large area of the parameter space. It is found that in most cases, the optimal direction of the in-plane magnetic field tends to be roughly parallel to the a -axis. This result, together with the fact that the orbital pair-breaking effect is weakest for ϕ = 0, implies that the FFLO state is most stabilized for a small ϕ . However, when the warp is small while the shear distortion is moderate, the FFLO state can be maximally stabilized for any in-plane magnetic-field direction except for the directions between the b - and b ′-axes, where the b ′-axis is perpendicular to the a -axis. The phase diagrams of the optimal angle and the upper critical field at zero temperature are also presented. A jump of the optimal angle ϕ 0 when the pressure varies is predicted.