As viable alternative light-harvesting materials in perovskite solar cells (PSCs), halide double perovskites (HDPs) Cs2BB'X-6 with B = monovalent cation and B' = trivalent cation have gathered extensive attention thanks to their excellent chemical stability and tunable properties. Unfortunately, most of these HDPs typically exhibit large optical bandgap and weak visible-light absorption, which seriously limits their application in single-junction PSCs. In this research, we theoretically report two novel Cs2HgPdX6 (X = Cl, Br) HDPs for the first time, and their interesting physical properties are scrutinized. According to our predictions, novel Cs2HgPdX6 (X = Cl, Br) is an experimentally synthesizable compound since its stability is carefully examined. Our calculations disclose that Cs2HgPdX6 (X = Cl, Br) is an indirect and large band gap compound (> 2 eV), and the band edges of valence and conduction bands mainly involve the strong orbital hybridization between Pd-4d and X-p. Additionally, under the application of pressure, the band gaps of both compounds are narrowed to an optimal value at moderate pressure, making them ideal alternatives for single-junction PSCs. The band gap reduction is due to the contraction of long Pd-X bond length and the increase of atomic orbital overlap. Meanwhile, the remarkable photochromic response of Cs2HgPdX6 (X = Cl, Br) with pressure is presented from the observations of the red-shift optical absorption spectra, thus it shows an obvious improvement for efficient visible-light absorption. Our study ensures the possibility of the application of pressure-induced Cs2HgPdX6 (X = Cl, Br) in the field of PSCs.