In this work, we have studied the effect of annealing temperature (T-S) on the structural properties and the critical behavior of Nd0.5Sr0.5MnO3 compound prepared by sol-gel method (T-S = 600, 700, 800 and 1000 degrees C). Scanning electronic microscope images indicate that all the samples are nanosized. The refinement of X-ray diffraction data shows that the samples sintered at 600 degrees C and 700 degrees C have three structural phases and that the monoclinic phase is linked to a superstructure (superlattice). The samples sintered at 800 degrees C and 1000 degrees C crystallize in the orthorhombic structure with Pnma space group, indicating the occurrence of a structural transition with increasing particle size. The magnetic measurements reveal that all our samples exhibit a paramagnetic to ferromagnetic transition with the absence of the long-range charge-ordered antiferromagnetic state. Through the magnetic field dependent magnetization, the observed overlapping between the isotherms suggests the persistence of some antiferromagnetic ordering in the nanosized samples. The reduction of saturation magnetization at 5 K for the sample sintered at 1000 degrees C indicates the beginning of the establishment of long-range charge ordering. The study of critical exponents has shown that the mean-field model is the most suitable model to describe the magnetic interactions for all our samples, suggesting the presence of long-range ferromagnetic interactions.