Berry phase physics is closely related to a number of topological states of matter.Recently discovered topological semimetals are believed to host a nontrivial π Berry phase,which is thought to induce a phase shift of ± 1/8 in the quantum oscillation (+ for hole and-for electron carriers).We theoretically study the Shubnikov-de Haas oscillation of topological Weyl and Dirac semimetals,taking into account their topological nature and inter-Landau band scattering.For Weyl semimetal with broken time-reversal symmetry,the phase shift can change smoothly but non-monotonically from ±1/8 near the Weyl nodes to ±5/8 at higher Fermi energies.For Dirac semimetal or paramagnetic Weyl semimetal,time-reversal symmetry leads to a discrete phase shift of ±1/8 or ±5/8,as a function of the Fermi energy.Different from the previous works,the topological band inversion can lead to beating patterns in the absence of Zeeman splitting.We also find the resistivity peaks should be assigned integers in the Landau index plot.Our findings may account for recent experiments in Cd2As3 and should be helpful for exploring the Berry phase in various 3D systems.