We study recovering sparse and compressible signals using lp minimization with p < 1 when some part of the support of the signal is known a priori. Sparse reconstruction method based on lp minimization with partially known set is proposed. Recovery conditions of lp minimization with partially known support is given. Theoretical results show that lp minimization with partially known set is stable and robust. Furthermore, numerical results show that lp minimization with partially known support needs fewer measurements than the standard compressed sensing with partially known support