By introducing a sub-terawatt (TW) laser pulse into a high-density gas target, the self-focusing effect and the self-modulation instability can greatly enhance the laser peak power to a level capable of driving the laser wakefield acceleration (LWFA) of electrons. A particle-in-cell model has been developed to study the scheme in which 1030-nm pulses produced from a diode-pumped laser system are introduced into a gas cell with a flat-top density profile, allowing the LWFA to be operated at high frequencies. Because 1030-nm lasers are typically produced with a long duration >200 fs, a spectral broadening technique can be applied to reduce the pulse duration, from which a greater ponderomotive force is acquired to drive LWFA. To understand the dependence of LWFA performance on the driving pulse duration, selected durations, ranging from 200 fs to 10 fs, are assigned for 0.5-TW, 1030-nm pulses in a series of simulations. Results show that a duration around 50 fs can provide the optimal LWFA results, as a compromise between the weak ponderomotive force available from a long pulse >100 fs and the depletion effect which can rapidly diminish a short pulse <25 fs in a dense plasma. When a low laser peak power of 0.25-TW is available, the pulse depletion can be significant at a high target density and render LWFA ineffective. Using a laser pulse with a longer wavelength >2 μm represents a viable route to realize the LWFA with a low laser peak power; in this way, an appropriately selected target density which allows the laser peak power PL ∼ 1.25Pcr of self-focusing critical power is favourable for realizing an efficient LWFA process.