Bound energy levels, up to 5000 cm(-1) of internal excitation, have been computed for the HFCO molecule. An exact six-dimensional (6D) quantum Hamiltonian, expressed in terms of Jacobi vectors, has been used. It is shown to lead to a compact form of the kinetic energy operator, easy to implement in the calculations. The primary discrete variable representation (DVR) basis set has been contracted by means of the adiabatic pseudospectral method of Friesner [J. Chem. Phys. 99, 324 (1993)]. Two different, global, potential energy surfaces have been considered. The calculated energy levels have been successfully assigned by an automatic labeling procedure. These levels have been compared to the experimental results, providing a test of the accuracy of the existing surfaces.