This paper gives the local existence of mild solutions to the Cauchy problem for the complex Ginzburg-Landau type equation ∂u ∂t − (λ + iα)∆u + (κ + iβ)|u| q−1 u − γu = 0 in R N × (0, ∞) with L p -initial data u0 in the subcritical case (1 6 q < 1 + 2p/N), where u is a complex-valued unknown function, α, β, γ, κ ∈ R, λ > 0, p > 1, i = √ −1 and N ∈ N. The proof is based on the L p -L q estimates of the linear semigroup {exp(t(λ + iα)∆)} and usual fixed-point argument.