Superconductivity close to charge ordering in quasi-two-dimensional 3/4-filled organic compounds is investigated for the theta-type structure. The effect of spin and charge fluctuations is calculated within random phase approximation for a relevant extended Hubbard model with both on-site (U) and intersite (V) Coulomb interactions on an anisotropic triangular lattice. It is found that both spin and charge fluctuations induce superconductivity with extended s-wave singlet pairing, which-is similar to the d(xy) pairing state in the square lattice. In the vicinity of charge-density-wave instability, f-wave triplet pairing is also stable due to the effect of nearest-neighbor Coulomb interaction. The temperature dependences of superconductivity and charge-density-wave phase boundaries are also examined.