We investigate fluctuation effects in a single-component ultracold Fermi gas with a p-wave interaction. Within the framework of a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) at the superfluid phase transition temperature Tc. Starting from the weak-coupling regime, we show that the so-called pseudogap structure develops in DOS, with increasing the strength of a pairing interaction. However, in contrast to the case of s-wave interaction (where the pseudogap size in DOS monotonically increases with increasing the interaction strength), the pseudogap structure is found to gradually disappear in the strong-coupling regime. We point out that this non-monotonic behavior of pseudogap originates from the momentum dependence of p-wave interaction. Our results clarify how the symmetry of pairing interaction affects pseudogap phenomena in strongly correlated fermion systems.