Abstract We synthesized the powder samples of KMg x Cu 5− x V 3O 13 ( x=0.1∼1) and investigated their magnetic susceptibilities and the magnetization curves up to 47 T. The Curie constant and the Weiss temperature of KMgCu 4V 3O 13 change markedly around 20 K. From the Curie constant estimated from the data between 5 and 10 K, the number of spins in the low-temperature region was estimated to be n low=8.13%, assuming all the copper spins have S=1/2 and g=2. The magnetization curve of KMgCu 4V 3O 13 at 1.7 K is bent around 20 T and shows a linear increase between 20 and 30 T. The magnetization, M linear( H→0), estimated by extrapolating the linear part to 0 T is 0.306 μ B/f.u. Furthermore, all the x dependences of the Néel temperature T N, n low, θ low, the magnetic field at spin–flop transition H sf and M linear( H→0) change continuously with x. This indicates that there is no quantum critical region between the frustrated spin chains of KCu 5V 3O 13 and KMgCu 4V 3O 13. The ground states of KCu 5V 3O 13 and KMgCu 4V 3O 13 have been deduced.