S=1/2 quasi-one-dimensional competing spin chain Cs2Cu2Mo3O12 has two dominant exchange interactions of the nearest-neighboring ferromagnetic J1 and the second nearest-neighboring antiferromagnetic J2. Due to the frustration effect, an exotic ground state is expected. So far, existence of the long range magnetic order at TN =1.85 K was reported by the specific heat at zero-field, NMR peak broadening, and an abrupt increase in lambda of ZF-muSR. Although these results assure an evidence of long range magnetic order, the static hyperfine field in the ordered state obtained by NMR becomes extremely small at low fields below 2 T, suggesting that the zero-field ordered state may be an unconventional one, such as the partial order. We would like to propose LF-muSR measurements in order to investigate the spin state, particularly its dynamical fluctuation at temperatures below TN.