We present results for phase structure of lattice QCD with two degenerate flavors ($N_f=2$) of Wilson quarks at finite temperature $T$ and small baryon chemical potential ${\mu }_B$. Using the imaginary chemical potential for which the fermion determinant is positive, we perform simulations at points where the ratios of pseudoscalar meson mass to the vector meson mass $m_{\pi }/m_{\rho }$ are between 0.943(3) and 0.899(4) as well as in the quenched limit. By analytic continuation to real quark chemical potential $\mu$, we obtain the transition temperature as a function of small ${\mu }_B$. We attempt to determine the nature of transition at imaginary chemical potential by histogram, Monte Carlo (MC) history, and finite size scaling. In the infinite heavy quark limit, the transition is of first order. At intermediate values of quark mass $m_q$ corresponding to the ratio of $m_{\pi }/m_{\rho }$ in the range from 0.943(3) to 0.899(4) at $a{\mu }_I=0.24$, the MC simulations show the absence of phase transition.

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