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The linear behavior of plasmoid instability in double current sheet configurations, namely, double plasmoid mode (DPM), is analytically and numerically investigated within the framework of a reduced magnetohydrodynamic model. Analytical analysis shows that if the separation of double current sheets is sufficiently small [ κxs«κ2/9S1/3L], the growth rate of DPMs scales as κ2/3S0L in the non-constant-ψregime, where κ=kLCS/2 is the wave vector measured by the half length of the system LCS/2, 2s is the separation between two resonant surfaces, and SL=LCSVA/2κ is Lundquist number with VA and η being Alfven velocity and resistivity, respectively. If the separation is very large [κxs»κ2/9S1/3L], the growth rate scales as κ-2/5S2/5L in the constant-ψ regime. Furthermore, it is also analytically found that the maximum wave number scales as xs-9/7sS3/7L at the transition position between these two regimes, and the corresponding maximum growth rate scales as xs-6/7SL-2/7there. The analytically predicted scalings are verified in some limits through direct numerical calculations. [ABSTRACT FROM AUTHOR]