In this paper, we investigate Kukles homogeneous systems ẋ=−y,ẏ=x+Qn(x,y), where Qn(x,y) is a homogeneous polynomial of degree n. There are two conjectures on the center-focus problem and isochronous center problem of the above systems. These two conjectures are claimed to be proven in Giné et al. (2015,2017). However, the proofs may have some gaps, hence they are still open. The gaps of Giné et al. (2015,2017) have been shown in Guo et al. (2021). In this paper, we consider isochronous centers in the family of Kukles homogeneous systems symmetric about the y-axis of degree eight. By using Period Abel constants and Gröbner basis of polynomial systems, we obtain that there is only one isochronous center excepting the linear center.