  We have investigated magnetic properties of Rb$_2$Cu$_2$Mo$_3$O$_{12}$
powder. Temperature dependence of magnetic susceptibility and magnetic-field
dependence of magnetization have shown that this cuprate is a model compound of
a one-dimensional spin-1/2 Heisenberg system with ferromagnetic
first-nearest-neighbor (1NN) and antiferromagnetic second-nearest-neighbor
(2NN) competing interactions (competing system). Values of the 1NN and 2NN
interactions are estimated as $J_1 = -138$ K and $J_2 = 51$ K ($\alpha \equiv
J_2 / J_1 = -0.37$). This value of $\alpha$ suggests that the ground state is a
spin-singlet incommensurate state. In spite of relatively large $J_1$ and
$J_2$, no magnetic phase transition appears down to 2 K, while an
antiferromagnetic transition occurs in other model compounds of the competing
system with ferromagnetic 1NN interaction. For that reason,
Rb$_2$Cu$_2$Mo$_3$O$_{12}$ is an ideal model compound to study properties of
the incommensurate ground state that are unconfirmed experimentally.
