The modified Korteweg-de Vries equation on the line is considered. The initial function is a discontinuous and piece-wise constant step function, i.e. q(x,0)=cr for x>0 and q(x,0)=cl for xcr>0. The goal of this paper is to study the asymptotic behavior of the solution of the initial-value problem as t→+∞. Using the steepest descent method we deform the original oscillatory matrix Riemann-Hilbert problem to explicitly solvable model forms and show that the solution of the initial-value problem has different asymptotic behavior in different regions of the xt plane. In the regions x4cl2t+2cr2t the main term of asymptotics of the solution is equal to cl and cr, respectively. In the region (−6cl2+12cr2)t<x<(4cl2+2cr2)t the asymptotics of the solution takes the form of a modulated hyper-elliptic wave generated by an algebraic curve of genus 2. V. Kotlyarov and A. Minakov, 2012