We investigate superfluid properties of a two-component Fermi gas in the BCS-BEC crossover region. Including strong-coupling effects within a Gaussian fluctuation approximation, we self-consistently determine the superfluid order parameter and chemical potential at finite temperatures. Using these self-consistent solutions, we calculate single-particle excitations, as well as collective mode, over the entire BCS-BEC crossover region. As one increases the strength of a pairing interaction, we show that, while the single-particle excitation gap becomes large, the velocity of collective Goldstone mode becomes small. As a result, the origin of temperature dependence of a physical quantity continuously changes from single-particle excitations to collective excitations, as one passes through the BCS-BEC crossover region. To see this, we examine the superfluid density.