A new peach variety (Prunus persica) designated as ‘Vilmos’ is provided. ‘Vilmos’ forms attractive, high quality fruit that matures during the commercially important ‘Andross’ period, and demonstrates a capacity to maintain good on-tree fruit quality for up to 10 days following initial ripening, allowing delayed harvest and economically efficient single harvests. Further, ‘Vilmos’ fruit exhibits the desirable characteristics of being free from the red staining of the pit area of fruit flesh in addition to having low susceptibility to splitting or cracking of the fruit pit during ripening, while also having other desirable fruit characteristics that are substantially similar to ‘Andross’.