The bubble regime acceleration of electrons by a short pulse laser in a carbon nanotube (CNT) embedded plasma is investigated, employing two-dimensional Particle-in-Cell simulations. The laser converts the CNT placed on the laser axis into dense plasma and expels the electrons out, to form a co-moving positive charged sheet inside the bubble. The additional field generated due to sheet enhances the energy of the monoenergetic bunch by about 5% and their number by 5–20%. For a typical 40 fs, 7.5 × 1019 Wcm−2 pulse in an underdense plasma of density n0, CNT of thickness 25 nm and electron density 30n0, produces a monoenergetic bunch of 115 MeV with 5% energy spread. When CNT density is raised to 90n0, the energy gain, energy spread and accelerated charge increases further. The analytical framework supports these features.