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Here, we report the evolution of magnetic behavior in doped Ru-based perovskite structure of SrRu_1-xGa_xO₃ series. The parent SrRuO₃ has an orthorhombic-Pbnm structure which also sustained by Ga doping and also showing a significant change in a structural parameter at 300 K. Polycrystalline SrRuO₃ is known to as an itinerant ferromagnet (FM) with T_c ~ 160 K and having large bifurcation between Zero-field-cooled and field-cooled (FC) magnetization below T_c which is decrease by Ga doping. The inverse susceptibility (χ^-1) in paramagnetic (PM) state and high-temperature region fitted by modified Curie-Weiss law (CWL). Effective moment (µ_eff) and θ_p decreases by Ga doping. The χ^-1 (T) revealed some upward deviation by Ga doping from CWL behavior above T_c due to formation of FM clusters in the PM background which is characterized as Griffiths phase. Critical exponent fitting of FC magnetization of SrRuO₃ close to T_c has showing mean field type behavior (β = 0.5) which is increases by Ga doping. Isothermal magnetization at 5 K of SrRuO₃ is showing hysteresis which also sustained by Ga doping with decreasing saturation moment (µ_H). The Arrott's plots also give confirmation of FM nature with decreasing value of spontaneous magnetization (M_S).