We present data obtained with the Very Long Baseline Array (VLBA) at twelve epochs (one observation per month from January to December 2011) at 15 and 24 GHz for the nearby TeV blazar Markarian 421 (z=0.031). We investigate the inner jet structure on parsec scales through the study of model-fit components for each epoch. The structure of Mrk 421 is dominated by a compact (FWHM about 0.13 mas) and bright component, with a one sided jet detected out to about 10 mas. We identified 5-6 components in the jet which are consistent with being stationary during the 12-month period studied here. Significant flux density variations have been detected for the core component. From our results, we estimate a viewing angle 2^◦ < θ < 5^◦ and a different jet velocity for the radio and the high-energy emission regions, such that the respective Doppler factors are δ_r ∼ 3 and δ_h.e ∼ 14.