We study the magnetocaloric effect and critical behavior of a periodic Anderson-like organic polymer using Greens function theory, in which the localized f orbitals hybridize with the conduction orbitals at even sites.The field-induced metal-insulator transitions with the magnetic Grüneisen parameter showing 丨(T)h丨～T1 power-law critical behaviour are revealed, which provides a new thermodynamic means for probing quantum phase transitions.It is found that the competition of up-spin and down-spin hole excitations is responsible for the double peak structure of magnetic entropy change(-ΔS) for the dominant Kondo coupling case, implying a double magnetic cooling process via demagnetization, which follows a power law dependence of magnetic field h:-ΔS～hn.The local exponent n tends to 1 and 2 below and above Tc, while has a minimum 0.648 at Tc, which is close to-ΔS～h2/3 for conventional ferromagnets obeying the mean field theory.Δt Tc, the-ΔS～h curves with convex curvature superpose each other for small V values, which are separated by the large V case,distinguishing the RKKY interaction and Kondo coupling explicitly Furthermore, the critical scaling law n(Tc)=1+(β-1)/(β+γ)=1+1/δ(1-1/β) is related to the critical exponents (β, γ, and δ) extracted from the Arrott-Noakes equation of state and Kouvel-Fisher method, which fulfill the Widom scaling relationδ=1+γβ-1, indicating self-consistency and reliability of the obtained results.In addition, based on the scaling hypothesis through checking the scaling analysis of magnetization, the M-T-h curves collapse onto two independent universal branches below and above Tc.