We examine the magnitude and size evolution of bulgeless (discs with no-bulge or pseudo-bulge) galaxies up to z~0.9 in rest-frame B-band. Their evolution is compared to that of normal-discs (discs with classical-bulge). The study is done for luminous sources (M_B<=-20) in two equal-volume redshift-bins (0.4<=z<0.77 and 0.77<=z<1.0) and a local range (0.02<=z<0.05). The mean surface-brightness, from z_{mean}=0.89 to z_{mean}=0.04, shows a dimming of 0.79 mag for bulgeless galaxies and 1.16 mag for normal-discs. The characteristic magnitude, M_B^*, shows an increase of 0.55-mag for bulgeless galaxies and 0.95-mag for normal-discs. Both dimming and faintness observed since z~0.9 are more pronounced for the normal-discs by ~0.4-mag. The size-distribution is log-normal and both bulgeless and normal-discs show a slight increase in the mean value from z_{mean}=0.89 to z_{mean}=0.04. The proportion of bulgeless galaxies in the full disc sample undergoes a considerable decline with decrease in redshift. This along with the larger dimming and faintness seen for normal-discs suggests that some fraction of the bulgeless sources switch to the normal-disc morphology with time. To ascertain the validity of studying morphology in the optical, the properties of the galaxies observed in both rest-frame B and I-band are compared. The common sample is more luminous in the I-band but the sizes are larger in the B-band for more than 74 % of the sources. The variation in the sersic-index values of the galaxies in the two rest-bands is minor enough to have any affect on the morphological classification.