A series of nickel-chromium-ferrite NiFe2-xCrxO4 (with x = 1.25) nanoparticles (NPs) with a cubic spinel structure and with size d ranging from 1.6 to 47.7 nm was synthesized by the solution combustion method. A dual structure of all phonon modes revealed in Raman spectra is associated with metal cations of different types present in the spinel lattice sites. Mössbauer spectra of small NPs exhibit superparamagnetic behavior. However, the transition into the paramagnetic state occurs at a temperature that is unusually high for small particles (TN is about 240 K in the d = 4.5 nm NPs). The larger NPs with d > 20 nm do not exhibit superparamagnetic properties up to the Neel temperature. From the magnetic and Mössbauer data, the cation occupation of the tetrahedral (A) and octahedral [B] sites was determined (Fe0.75Ni0.25)[Ni0.75Cr1.25]O4. The saturation magnetization MS in the largest NPs is about (0.98-0.95) μB, which is more than twice higher the value in bulk ferrite (Fe)[CrNi]O4. At low temperatures the total magnetic moment of the ferrite coincides with the direction of the B-sublattice moment. In the NPs with d > 20 nm, the compensation of the magnetic moments of A- and B-sublattices was revealed at about Tcom = 360-365 K. This value significantly exceeds the point Tcom in bulk ferrites NiFexCr2-xO4 (about 315 K) with the similar Cr concentration. However, in the smaller NPs NiFe0.75Cr1.25O4 with d ≤ 11.7 nm, the compensation effect does not occur. The magnetic anomalies are explained in terms of highly frustrated magnetic ordering in the B sublattice, which appears due to the competition of AFM and FM exchange interactions and results in a canted magnetic structure.