Context. Knowing the exact shape of the ultraviolet (UV) luminosity function (LF) of high-redshift galaxies is important to understand the star formation history of the early Universe. However, the uncertainties, especially at the faint and bright ends of the LFs, remain significant. Aims: In this paper, we study the UV LF of redshift z = 2.5 - 4.5 galaxies in 2.38 deg2 of ALHAMBRA data with I ≤ 24. Thanks to the large area covered by ALHAMBRA, we particularly constrain the bright end of the LF. We also calculate the cosmic variance and the corresponding bias values for our sample and derive their host dark matter halo masses. Methods: We have used a novel methodology based on redshift and magnitude probability distribution functions (PDFs). This methodology robustly takes into account the uncertainties due to redshift and magnitude errors, shot noise, and cosmic variance, and models the LF in two dimensions (z, MUV). Results: We find an excess of bright * M*UV galaxies as compared to the studies based on broad-band photometric data. However, our results agree well with the LF of the magnitude-selected spectroscopic VVDS data. We measure high bias values, b 8 - 10, that are compatible with the previous measurements considering the redshifts and magnitudes of our galaxies and further reinforce the real high-redshift nature of our bright galaxies. Conclusions: We call into question the shape of the LF at its bright end; is it a double power-law as suggested by the recent broad-band photometric studies or rather a brighter Schechter function, as suggested by our multi-filter analysis and the spectroscopic VVDS data. Based on observations collected at the German-Spanish Astronomical Center, Calar Alto (CAHA), jointly operated by the Max-Planck-Institut fur Astronomie (MPIA) at Heidelberg and the Instituto de Astrofísica de Andalucía (CSIC).