We estimate the abundance of the coherent oscillation of moduli, which linearly couple to matter fields through higher dimensional operators. During the (p)reheating after inflation, matter particles are efficiently produced and it can affect the moduli potential in a non-adiabatic way, which results in the coherent oscillation of the moduli. In particular, such effects are most important at the very beginning of the (p)reheating. It is found that this production mechanism is so efficient that a successful evolution of the universe can be threatened even if the moduli mass is larger than the Hubble scale.1 Without loss of generality, we choose the zero-temperature potential minimum of the modulus as σ = 0.2 Even in the case of C 1 [11], the modulus amplitude is not suppressed enough [12]. 3 The effect of linear term proportional to T 4 on the modulus oscillation, where T denotes the temperature, was discussed in the context of moduli [13] and flavon [14] for the case of m σ < H inf . See also an earlier work [15].