A central issue on high-T{sub c} superconductivity is the nature of the normal-state gap (pseudogap) in the underdoped regime and its relationship with superconductivity. Despite persistent efforts, theoretical ideas for the pseudogap evolve around fluctuating superconductivity, competing order and spectral weight suppression due to many-body effects. Recently, while some experiments in the superconducting state indicate a distinction between the superconducting gap and pseudogap, others in the normal state, either by extrapolation from high-temperature data or directly from La{sub 1.875}Ba{sub 0.125}CuO{sub 4} (LBCO-1/8) at low temperature, suggest the ground-state pseudogap is a single gap of d-wave form. Here we report angle-resolved photoemission (ARPES) data from LBCO-1/8, collected with improved experimental conditions, that reveal the ground-state pseudogap has a pronounced deviation from the simple d-wave form. It contains two distinct components: a d-wave component within an extended region around the node and the other abruptly enhanced close to the antinode, pointing to a dual nature of the pseudogap in this failed high-T{sub c} superconductor which involves a possible precursor pairing energy scale around the node and another of different but unknown origin near the antinode. Show Partial Abstract