This paper studies the metrizability of the notion of L-topological groups defined by Ahsanullah. We show that for any (separated) L-topological group there is an L-pseudo-metric (L-metric), in sense of G¨ahler which is defined using his notion of L-real numbers, compatible with the L- topology of this (separated) L-topological group. That is, any (separated) L-topological group is pseudo-metrizable (metrizable). Keywords: Countable L-filters; Countable L-topological spaces; L-topological groups; Separated L-topological groups; L-metric spaces; L-pseudo-metric spaces; L-uniform spaces; L-filters.