In a study of decagonal quasicrystals and crystalline approximants in the Al-rich binary Al-Co alloy, a new monoclinic crystalline phase has been found in an alloy with a composition of Al-11-Co-4 after slow solidification from the melt. The crystal structure of this Al11Co4 approximant (with a stoichiometric composition Al73.24Co26.76) has been determined by single-crystal X-ray analysis. It has a monoclinic lattice with a = 2.4661(5)nm, b = 0.4056(9) nm, c = 0.7569(2) nm, beta = 107.88(3)degrees, a space group of P2, 52 atoms in one unit cell and a density of 4.26 Mg m(-3). A final R factor of 0.088 has been achieved for 718 reflections. The structure can be viewed as an alternate stacking of flat and puckered layers along its b axis and can be characterized as a two-dimensional period arrangement of pentagonal atomic columns. It has a close structural relationship to both the Al13Co4 and the Al13Os4 phases. The structures oi Al-Co and Al-Cu-Co decagonal quasicrystals with space groups P10(5)/mmc and P10m2 respectively, are discussed on the basis of these crystalline structures.