We discuss the nature of the phase transition for lattice QCD at finite temperature and density. We propose a method to calculate the canonical partition function by fixing the total quark number introducing approximations allowed in the low density region. An effective potential as a function of the quark number density is discussed from the canonical partition function. We analyze data obtained in a simulation of two-flavor QCD using p4-improved staggered quarks with bare quark mass $m/T = 0.4$ on a $16^3 \times 4$ lattice. The results suggest that the finite density phase transition at low temperature is of first order.