Band structure of a body-centered cubic (BCC) lithium with a hydrogen atom doped in at room temperature is calculated within local density approximation (LDA) under density functional theory (DFT) framework. The distorted band structure induced by the dopant hydrogen atom has been found in comparing with pure lithium. A new ionic band is formed mainly from s state of hydrogen atom with hybridizing a little portion of s and p state of lithium atoms. The hydrogen atom captures one valence electron from lithium atoms due to this ionic band, forming an anion. The electronic states of lithium are dominant for the metallic s-bands near Fermi Level and all p-bands, keeping the doped system with metallic features. The electron energy loss (EEL) spectrum of the pure system is changed by the hydrogen impurity, not only in the amplitudes but also in the locations of main peaks.