As a promising piezoelectric system with high ferroelectric Curie temperature (TC) and stable perovskite structure, the (1-x)BiFeO3-xPbTiO3 (BF-xPT) binary solid solution has attracted increasing interest as high-temperature piezoelectrics. In this work, a series of BF-xPT single crystals with different compositions have been successfully grown using high temperature solution method. Structural characterization by powder X-ray diffraction (XRD) shows a crossover with increasing x from a dominant rhombohedral R3c phase to a pure P4mm phase. The TC determined from the temperature dependence of dielectric constant decreases with increasing PT concentration, from 675 oC to 525 oC. By comparing the lattice parameters and TC of single crystals with those of polycrystalline ceramics, the actual compositions of the as-grown single crystals have been determined. The static domain structures have been studied by various techniques, including etching method, Polarized Light Microscopy (PLM) and Piezoresponse Force Microscopy (PFM). The switching behaviors of domains under electric field and their evolution with temperature have been investigated and discussed using PFM and PLM, respectively. The difference between domain patterns inside and domain structures on the surface of the single crystal platelets supports the existence of a skin layer. In addition, our single crystals of good quality enable the application of high enough electric field to obtain the square-shaped ferroelectric hysteresis loops.