The laser wakefield acceleration in bubble regime is now a promising method for producing high-quality electron beams, which is crucial to the development of the next-generation compact and low-cost particle accelerators. In this paper, we demonstrate the possibility of controlling particle injection and electron beam quality in sub-petawatt laser pulse interaction with simple plasma waveguides with a radially step-like density profile. Fully relativistic particle-in-cell calculations for different laser intensities indicate that by considering a sufficiently low electron density for a central plasma channel to ensure both increased acceleration length and formation of a well-structured bubble, one can optimize the surrounding plasma density and central channel diameter to reach the best injection conditions and produce a high-quality monoenergetic electron beam with improved peak energy and reduced energy spread. Calculations are performed for 33 fs, 140–315 TW laser pulses interacting with a ∼2 cm long plasma waveguide. It is demonstrated that by using the proposed scheme in optimized conditions, monoenergetic electron beams with peak energies 3–4 GeV and energy spreads less than 1.5% can be obtained in a single acceleration length of 1.85 cm. The beam charge and conversion efficiency of laser energy into the beam energy were also enhanced to values around 195 pC and 14.7%, respectively.