The complete active space self-consistent field and multiconfigurational second-order perturbation theory methods have been used to investigate the low-lying electronic states of the HCCO radical and its anion. The calculated geometrical structure and harmonic vibrational frequencies for the X(2)A '' state of HCCO are in good agreement with experimental values. The barrier to 1(2)Pi (1(2)A') is estimated to be 0.069 eV (554 cm(-1)), which is also close to experimental result (540 cm(-1)). Moreover, we find that the 2(2)A' state is bent, while 2(2)Pi (2(2)A '') is linear. By comparing the oscillator strengths and adiabatic excitation energies, we show that the 2(2)Pi (2(2)A '') <- X(2)A '' transition is the most intense among these transitions. The unpaired electrons mainly locate on the C atoms in the 2(2)A' and 2(2)Pi (2(2)A '') states according to the Mulliken spin populations. On the other hand, for HCCO-, the first adiabatic and vertical detachment energies are 2.210 and 2.362 eV, respectively, which reasonably agree with experimental value of 2.338 +/- 0.008 eV. Remarkably, we explore several higher excited states of the HCCO radical (1(4)A', 2(4)A '' and cis-1(4)A') and its anion (1(3)A '', 1(1)A '' and 1(3)A'), which have not been reported in previous studies.