The purpose of this work is to study the L 2 −critical focusing inhomogeneous nonlinear Schrödinger equationWe study the dynamical behavior for blow-up solutions when initial date ∈ H 1 (R N ) and satisfies || || L 2 ≥ ||Q|| L 2 , where Q is the ground state solution of our problem. Furthermore, we obtain the determination of the blow-up solutions when || || L 2 = ||Q|| L 2 . KEYWORDS blow-up, dynamical behavior, profile decomposition 9408