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The integrated Sachs-Wolfe (ISW) effect is an important implication for darkenergy. In this paper, we have calculated the power spectrum of the ISW effectin the time varying vacuum cosmological model, where the model parameter$\beta=4.407$ is obtained by the observational constraint of the growth rate.It's found that the source of the ISW effect is not only affected by thedifferent evolutions of the Hubble function $H(a)$ and the dimensionless matterdensity $\Omega_m(a)$, but also by the different growth function $D_+(a)$, allof which are changed due to the presence of matter production term in the timevarying vacuum model. However, the difference of the ISW effect in$\Lambda(t)\textmd{CDM}$ model and $\Lambda \textmd{CDM}$ model is lessened toa certain extent due to the integration from the time of last scattering to thepresent. It's implied that the observations of the galaxies with high redshiftare required to distinguish the two models.

The Integrated Sachs-Wolfe Effect in Time Varying Vacuum Model