Single crystals of Yb3(Rh1−xTx)4Ge13 (T=Co,Ir) have been grown using the self-flux method. Powder x-ray diffraction data on these compounds are consistent with the cubic structure with space group Pm3¯n. Intermediate-valence behavior is observed in Yb3(Rh1−xTx)4Ge13 upon T = Co doping, while T = Ir doping drives the system into a heavy-fermion state. Antiferromagnetic order is observed in the Ir-doped samples Yb3(Rh1−xTx)4Ge13 for 0.5<x≤1 with TN=0.96 K for Yb3Ir4Ge13. With decreasing x, the magnetic order is suppressed towards a quantum critical point around xc = 0.5, accompanied by non-Fermi-liquid behavior evidenced by logarithmic divergence of the specific heat and linear temperature dependence of the resistivity. The Fermi-liquid behavior is recovered with the application of large magnetic fields.