Laser wakefield acceleration (LWFA) can be accomplished by introducing a sub-terawatt (TW) laser pulse into a thin, high-density gas target. In this way, the self-focusing effect and the self-modulation that happened on the laser pulse produce a greatly enhanced laser peak intensity that can drive a nonlinear plasma wave to accelerate electrons. A particle-in-cell model is developed to study sub-TW LWFA when a 0.6-TW laser pulse interacts with a dense hydrogen plasma. Gas targets having a Gaussian density profile or a flat-top distribution are defined for investigating the properties of sub-TW LWFA when conducting with a gas jet or a gas cell. In addition to using 800-nm laser pulses, simulations are performed with 1030-nm laser pulses, as they represent a viable approach to realize the sub-TW LWFA driven by high-frequency, diode-pumped laser systems. The peak density which allows the laser peak power PL∼2Pcr of self-focusing critical power is favourable for conducting sub-TW LWFA. Otherwise, an excessively high peak density can induce an undesired filament effect which rapidly disintegrates the laser field envelope and violates the process of plasma wave excitation. The plateau region of a flat-top density distribution allows the self-focusing and the self-modulation of the laser pulse to develop, from which well-established plasma bubbles can be produced to accelerate electrons. The process of electron injection is complicated in such high-density plasma conditions; however, increasing the length of the plateau region represents a straightforward method to realize the injection and acceleration of electrons within the first bubble, such that an improved LWFA performance can be accomplished.