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A new Nd³⁺-doped CaGdAlO₄ laser crystal was investigated. This crystal was grown by the Czochralski method. The atomic concentration of Nd³⁺ in the melt was 2%. The absorption and luminescence spectra were analysed and the Stark structure of the upper and lower active levels was determined. The lifetime of the upper level was ≈140 μs. The stimulated emission cross section at the 1078 nm wavelength was 1.1 × 10^-19cm² for the polarisation. A GaAlAs diode, with an output power of 3 W emitting at the wavelength 806.5 nm, was used as the pump source. The slope efficiency was 37% at the 1078 nm wavelength when the output mirror transmission was 5%. The output radiation power of the crystal laser was 360 mW when the absorbed pump power was 1.29 W.