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We study the phase transition between pion condensed phase and normal phase,as well as chiral phase transition in a two flavor($\mathcal{N}_f=2$) IR-improved soft-wall AdS/QCD model at finite isospin chemical potential $\mu_I$and temperature $T$. By self-consistently solving the equations of motion, weobtain the phase diagram in the plane of $\mu_I$ and $T$. The pion condensationappears together with a massless Nambu-Goldstone boson $m_{\pi_1}(T_c,\mu_I^c)=0$, which is very likely to be a second-order phase transition withmean-field critical exponents in small $\mu_I$ region. When $T=0$, the criticalisospin chemical potential approximates to vacuum pion mass $\mu_I^c \approxm_0$. The pion condensed phase exists in an arched area and the boundary of thechiral crossover intersects the pion condensed phase at a tri-critical point.Qualitatively, the results are in good agreement with previous studies fromLattice simulations and model calculations.

QCD phase diagram at finite isospin chemical potential and temperature in an IR-improved soft-wall AdS/QCD model