Ternary CoFeNi-layered double hydroxide (CoFeNi-LDH) was synthesized and initially applied to activate peroxymonosulfate (PMS) for the degradation of Congo red (CR) and Rhodamine B (RhB). The results show that the CoFeNi-LDH/PMS system can efficiently degrade nearly 100% of 20 mg/L CR or 20 mg/L RhB within 6- and 10-min reaction times, respectively. And the catalyst exhibits higher degradation efficiency on CR than on RhB under identical conditions, which is confirmed by electron clouds of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) performed by DFT calculations. Quenching tests reveal that SO4-center dot is the dominant active species participating in the degradation process. Mechanism investigation demonstrates that Co(II)-Co(III)-Co(II) cycle is responsible for activating PMS to generate radicals for dyes degradation. A dynamic kinetic model is successfully developed to simulate the concentration profiles of CR and RhB degradation in CoFeNi-LDH/PMS system. The empirical second order rate constants between SO4-center dot and CR (k(SO4-center dot/CR)), HO center dot and CR (k(center dot OH/CR)). SO4-center dot and RhB (k(SO4-center dot/RhB)), HO center dot and RhB (k(HO center dot/RhB)) are determined to be 2.47 x 10(7), 3.44 x 10(6), 8.39 x 10(6) and 2.62 x 10(7) M(-1)s(-1), respectively. In addition, toxic assessment using ECOSAR program suggests that the overall toxicity of CR and RhB decreased after treatment with CoFeNi-LDHIPMS system. Repeating tests and application of CoFeNi-LDH in different water sources give us adequate confidence that the as synthesized CoFeNi-LDH is favorable for the purification of dye-contaminanted waters in practical. (C) 2018 Published by Elsevier Inc.