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In recent years, two-dimensional (2D) metal halide perovskites have emerged at the forefront of materials science and optoelectronics, owing to their remarkable electronic properties and enhanced stability in comparison to their 3D counterparts. Despite the crucial role played by charge transport in their optoelectronic applications, research on the intrinsic transport behavior, in particular the photoconductivity, of the 2D halide perovskites, has been lacking due to their high resistivity, large contact resistances, and the influence of ion migration. Here, we studied the transport behavior of 2D halide perovskite (PEA)₂PbI₄ single crystals by reliable 4-terminal measurements from room temperature to 1.6 K. Linear I-V characteristics without visible hysteresis in the whole temperature range indicate that ion migration in our materials is negligible. Temperature dependence of the photoconductivity shows a transition near 140 K, which could be tuned by electrostatic gating via a bottom gate. Notably, our experimental results suggest that the photocurrent in the 2D halide perovskites occur via band transport, rather than hopping mechanisms, even at low temperatures, despite their very high resistivity. This work filled an important gap in the transport study of 2D metal halide perovskites, which provides valuable insight on their intrinsic transport properties and useful guidelines for device applications.