The NdCrO3 perovskite nanoparticles have been successfully synthesized using sol-gel auto-combustion process. Structural and morphological characterizations of the material have been performed at room temperature using XRD and SEM, respectively. Frequency- and temperature-dependent dielectric measurements have been performed in the range of 1Hz-10MHz and RT -300 degrees C, respectively. The dielectric constant is found to be in the order of epsilon>10(3) at room temperature, indicating the colossal dielectric constant behaviour. Ferroelectric phase transition temperature has increased with an increase in frequency, suggesting that the material is a relaxor ferroelectric nature. Temperature- and field-dependent magnetization measurements have been carried out in the temperature range (5-400K) and field up to 5T. M-T curve exhibited a diamagnetic-like behaviour in low temperature and low fields. Two magnetic transitions were found at T-N1 (223K) and T-N2 (33K) which correspond to para to weak ferromagnetic transition and Nd3+ spin ordering, respectively. Hysteresis loop noticed weak ferromagnetism.