We report on a comparative study of the structural, magnetic, and dielectric and properties of isovalent and aliovalent A-site substituted Sr2-xAxCrMoO6 (A = Ca, x = 0.0, 0.1, 0.3, 0.5, 0.7, 0.8, 1.0; A = K, La only x = 0.5) double perovskites, which were synthesized via sol-gel process. X-ray diffraction patterns and Rietveld refinements demonstrated that all the Sr2-xAxCrMoO6 powders crystallized in a cubic crystal structure with space group of Fm3‾m. SEM images revealed that the Sr2-xAxCrMoO6 powders exhibited a spherical morphology. Their chemical compositions were determined by quantitative energy dispersive X-ray spectroscopy, which were close to the nominal values. FTIR spectra analyses verified the presence of (Cr, Mo)O6 octahedra in these powders. XPS spectra validated the existence of Sr2+, K+, Ca2+, La3+, and Cr3+ ions in the powders, and oxygen existed in the forms of lattice oxygen and absorbed oxygen respectively, whereas Mo element had a mixed chemical valence state of Mo4+ and Mo6+. The Sr2CrMoO6 (SCMO) powders had a saturation magnetization (MS) of 0.016 μB/f.u. at 2 K, magnetic Curie temperature (TC) of 337 K, and irreversibility temperature (Tirr) of 329 K where the zero-field cooled (ZFC) and field-cooled (FC) magnetization (MZFC and MFC, respectively) curves became bifurcated. A spin-glass behavior was observed at temperature (TB) of 81 K. Both Tirr and TB shifted towards low temperature with increasing the external magnetic field. In addition, the MZFC and MFC curves became almost overlapped under the external field of 50 kOe, and the spin-glass behavior disappeared. The M-H data demonstrated that both isovalent and aliovalent A-site substitutions could improve the magnetic properties and B-site ordering degree (η) of the SCMO powders. However, isovalent Ca-substitution exhibited more significant enhanced effect on the magnetic properties in comparison with the aliovalent A-site substitutions either by K- or La-substitution. Among the isovalent Ca-substituted Sr2-xCaxCrMoO6 (x = 0.1–1.0) powders, Sr1.2Ca0.8CrMoO6 sample had a maximum MS value of 0.64 μB/f.u. at 2 K, over 30 times enhancement of that of the pristine SCMO powders. The Sr2-xAxCrMoO6 ceramics exhibit a strong frequency dependent dielectric behavior, which can be well interpreted by Maxwell-Wagner relaxation model. The anomalous dielectric relaxor behavior of the SCMO ceramics observed at 260 K was ascribed to the jumping of the electrons trapped in a shallower energy level created by oxygen vacancies. The dielectric constant of the isovalent Ca-substituted Sr1.5Ca0.5CrMoO6 samples was 30 times larger than that of the pristine SCMO samples. Our present results demonstrate that isovalent Ca-substitution at A-site could improve the magnetic and dielectric properties of the sol-gel derived SCMO double perovskite oxides, which have potential applications in the fields of spintronic devices and dielectric devices.