The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is examined in quasi-one-dimensional s-wave and d-wave superconductors with particular attention paid to the effect of the Fermi-surface anisotropy. The upper critical field H c2 (T ) is found to exhibit a qualitatively different behavior depending on the ratio of the hopping energies t b /t a and the direction of the FFLO modulation vector q, where t a and t b are the intra-and interchain hopping energies, respectively. In particular, when t b /t a < ∼ 0.1 and q a, we find a novel dimensional crossover of H c2 (T ) from one dimension to two dimensions, where a is the lattice vector of the most conductive chain. Just below the tricritical temperature T * , the upper critical field H c2 (T ) increases steeply as in one-dimensional systems, but when the temperature decreases, the rate of increase in H c2 (T ) diminishes and a shoulder appears. Near T = 0, H c2 (T ) shows a behavior typical of the FFLO state in two-dimensional systems, i.e., an upturn with a finite field at T = 0. When the angle between q and a is large, the upper critical field curve is convex upward at low temperatures, as in three-dimensional systems, but the magnitude is much larger than that of a three-dimensional isotropic system. For t b /t a > ∼ 0.15, the upper critical fields exhibit a two-dimensional behavior, except for a slight shoulder in the range of 0.2 > ∼ t b /t a > ∼ 0.15. The upper critical field is maximum for q a both for s-wave and d-wave pairings, while it is only slightly larger than the Pauli paramagnetic limit for q ⊥ a. The relevance of the present results to the organic superconductor (TMTSF) 2 ClO 4 is discussed.