In this paper, three new efficient Eu3+-activated Ca2EuMO6 (M = Sb, Nb, and Ta) red-emitting phosphors with outstanding luminescence properties were prepared by using the high-temperature solid-state reaction method. X-ray diffraction and Rietveld refinements revealed the double-perovskite structure of Ca2EuMO6 (M = Sb, Nb, and Ta) compounds. Photoluminescent excitation and emission spectra, decay lifetimes, CIE chromaticity coordinates, color purity values, internal quantum efficiency, and thermal stability were discussed in detail. Under the excitation of 395 nm near-ultraviolet light, these Ca2EuMO6 (M = Sb, Nb, and Ta) phosphors demonstrated bright narrow-band red emissions with peaks at 592, 620, 656, and 703 nm due to the 5D0→7FJ (J = 1–4) transitions of Eu3+ ions. The internal quantum efficiencies of the Ca2EuSbO6, Ca2EuNbO6, and Ca2EuTaO6 samples were determined to be 39.3%, 41.6%, and 40.4%, respectively. Impressively, the emission intensity of Ca2EuNbO6 is about 1.25 times higher than that of commercial Y2O3:Eu3+ red phosphor. CIE color coordinates of Ca2EuMO6 (M = Sb, Nb, and Ta) phosphors were calculated to be (0.6748, 0.3250), (0.6800, 0.3198), and (0.6790, 0.3208), respectively; along with high color purity of 90.7%, 93.2%, and 92.7%. Besides, their thermal stability was also investigated, and the corresponding emission intensities of Ca2EuMO6 (M = Sb, Nb, and Ta) at 423 K were respectively maintained at 73%, 86%, and 80% of that at 303 K. All results show that these newly developed red-emitting Ca2EuMO6 (M = Sb, Nb, and Ta) phosphors possess potential applications in white light-emitting diodes.