In mammals, some embryonic genes are expressed differently depending on whether they are inherited from the sperm or egg, a phenomenon known as genomic imprinting. The information on the parental origin is transmitted by an epigenetic mark. Both the molecular mechanisms and evolutionary processes of genomic imprinting have been studied extensively. Here, I illustrate the simplest evolutionary dynamics of imprinting evolution based on the "conflict theory," by considering the evolution of a gene encoding an embryonic growth factor controlling the maternal resource supply. It demonstrates that (a) the autosomal genes controlling placenta development to modify maternal resource acquisition may evolve a strong asymmetry of gene expression, provided the mother has some chance of accepting multiple males. (b) The genomic imprinting may not evolve if there is a small fraction of recessive deleterious mutations on the gene. (c) The growth-enhancing genes should evolve to paternally expressed, while the growth-suppressing genes should evolve to maternally expressed. (d) The X-linked genes also evolve genomic imprinting, but the main evolutionary force is the sex difference in the optimal embryonic size. I discuss other aberrations that can be explained by the modified versions of the basic model.