Halide double perovskites A2B(I)B(III)X6, in which monovalent B(I) and trivalent B(III) cations are arranged in the B-sites of the perovskite structure with a rock-salt ordering, have attracted substantial interest in the field of optoelectronics. However, the rock-salt ordering generally leads to low electronic dimensionality, with relatively large bandgaps and large carrier effective masses. In this work, we demonstrate, by density functional theory (DFT) calculations, that the electronic dimensionality and thus the electronic properties of halide double perovskites can be effectively modulated by manipulating the arrangement of the B-site cations. Through symmetry analysis and DFT calculations, we propose a family of halide double perovskites A2B(I)B(II)X5 where the B-site cations adopt a columnar-ordered arrangement. Among the considered compounds, Cs2AgPdCl5, Cs2AgPdBr5, and Cs2AgPtCl5 were successfully synthesized as the first examples of the B-site columnar-ordered halide double perovskites. These compounds exhibit small bandgaps of 1.33-1.77 eV that are suitable for visible light absorption, small carrier effective masses along the octahedra chains, and good thermal and air stability. Our work provides a prototype double perovskite structure to incorporate cations in +1 and +2 oxidation states, which may significantly expand the large family of the halide double perovskites and offer a platform to explore prospective optoelectronic semiconductors.