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.