Recently, Multiple Background Models (M-BMs) [1, 2] have been shown to be useful in speaker verification, where the M-BMs are formed based on different Vocal Tract Lengths (VTLs) among the population. The speaker models are adapted from the particular Background Model (BM) corresponding to their VTL. During test, log likelihood ratio of the test utterance is calculated between claimant model and the corresponding BM. In this paper, instead of using different BM for different speaker, we propose the use of single gender, channel and VTL independent UBM (root-UBM) using the concept of VTL dependent mapping function. The proposed concept is inspired by Feature Mapping (FM) technique used in speaker verification to overcome channel variability. In our proposed method, VTL specific gender independent Gaussian Mixture models (GMMs) are derived from the root-UBM using Maximum a posteriori (MAP) adaptation. The mapping relation is then learned between the root-UBM and the VTL-specific GMM...