In a recent article by Li et al (2019 Sci. Adv. 5. eaav7940), experimental results from a dual-color laser wakefield acceleration (LWFA) were presented. In the present paper we, primarily, focus on detailed simulation studies of such a scheme in the self-injection and ionization injection regimes, respectively. The spatiotemporally-overlapped 30 fs dual-color laser pulses are at fundamental (FL, 800 nm, 'red') and second-harmonic (SH, 400 nm, 'blue') wavelengths. They are (a) co-propagating in an under-dense plasma, (b) relativistically intense (I > 1018 W cm−2) and (c) having relatively high-energy (multi-Joule, loose focusing) and low-energy (sub-Joule, tight focusing), respectively. The basic concept of the scheme is the fact that the depletion length (Lpd) for a relativistic laser pulse in an under-dense plasma has an inverse quadratic dependence on the laser wavelength (∝1/λ2). Here, first by using a single FL 77 TW/30 fs laser pulse to drive a LWFA, an electron beam was accelerated up to ∼400 MeV from a background plasma having an electron density of 1019 cm−3. Then, by driving the same LWFA by co-propagating 'blue' 7 TW/30 fs and 'red' 70 TW/30 fs laser pulses, the electron energy reached ∼700–800 MeV (maximum). The simulations confirm that in such a dual-color LWFA scheme, the role of the SH laser pulse is post-accelerating electrons after a rapid depletion of the FL laser pulse in the plasma. Furthermore, the SH pulse assists the ionization-injection of the electrons which is an additional benefit of the dual-color LWFA scheme.