As a novel layered noble metal dichalcogenide material, palladium diselenide (PdSe2) has attracted wide interest due to its excellent optical and electronic properties. In this work, a strong third-order nonlinear optical response of 2D PdSe2 films is reported. We conduct both open-aperture (OA) and closed-aperture (CA) Z-scan measurements with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe2 film of β = 3.26 ×10-8 m/W. In the CA experiment, we measure a peak-valley response corresponding to a large and negative Kerr nonlinearity of n2 = -1.33×10-15 m2/W – two orders of magnitude larger than bulk silicon. In addition, the variation of n2 as a function of laser intensity is also characterized, with n2 decreasing in magnitude when increasing incident laser intensity, becoming saturated at n2 = -9.96×10-16 m2/W at high intensities. Our results show that the extraordinary third-order nonlinear optical properties of PdSe2 have strong potential for high-performance nonlinear photonic devices.