A period-doubling route to chaos with nonstationary transverse pattern is observed in a diode-pumped Nd:YAG laser with a Cr(4+):YAG saturable absorber. The nonlinear behavior results from the multitransversemode competition with gradually adding the number of the transverse modes. By analyzing the transverse pattern, we find that the bifurcation accompanies with the increase of the higher-order family of transverse modes in sequence. Moreover, a series of period-doubling route to chaos beginning from the low period is attained by varying the pump power at specific cavity configurations.