The measurements of temperature dependence of the magnetic susceptibility of La1-xSrxCoO3 perovskite oxides at different Sr doping (0≤x≤0.5) and annealing temperature were presented. For the sample with x=0.1, a shoulder was observed around 150 K, and a peak which is one feature of spin glass appeared around 50 K in the curve of susceptibility versus temperature. The high-temperature(250～420 K)susceptibility fits well with Curie-Weiss law for all samples. Weiss constant and effective magnetic moment were determined and their variations with Sr doping and oxygen annealing condition were obtained. The Weiss constant increases monotonously with Sr content for x>0.2. The values of effective moments were interpreted with the spin state of cobalt ions. Studies on the susceptibilities of the samples with x=0.2 under different preparation temperatures and annealing temperatures show that the rising of sintering temperature and annealing temperature will increase the para-ferromagnetic transition temperature, and reduce the effective moment to normal value. Our result shows that both Co3+ and Co4+ ions should be in IS state after annealing and the oxygen annealing causes the transition of Co3+ spin state from HS to IS.