The linear properties of both even and odd double tearing modes (DTMs) in the presence of plasma shear flow are studied based on a reduced resistive MHD model in slab geometry. It is found that for the anti-symmetric shear flow, the linear growth rates γ(ky) of the even (odd) eigenmode of DTMs decrease (increase) with increasing the strength of shear flow. Indeed, in the small wavenumber ky regime, γ(ky) of the even eigenmode is larger than that of the odd eigenmode, while γ(ky) of two kinds of eigen states coalesce with each other (the same growth rate and opposite frequencies) when the wavenumber ky exceeds a critical value kyC. It is demonstrated that kyC decreases with decreasing η for a fixed separation between two resonant surfaces xs, while decreasing xs increases the critical value of kyC for a fixed shear velocity. In the nonlinear regime for a low value of resistivity, it is observed that by increasing the strength of anti-symmetric shear flow, in the early phase of the abrupt regime a monster plasmoid and subsidary small plasmoids are generated, and later they are ejected from the DTM current sheet and merged with the main DTM islands.