A 3-5 GHz broadband CMOS single-ended LNA with a new theoretical approach based on least-square algorithm is presented in this paper. The design consists of a wideband input impedance matching network, a cascoded amplifier with inductively-degenerated LNA, and an output impedance matching network. It is simulated in TSMC 0.18 μm standard RF CMOS process. The optimum matching network is designed to minimize the noise figure (NF) and maximize the power gain. The element values of optimum matching network have been obtained using the least-square algorithm. The proposed LNA exhibits a gain in range of 19.9-18.9 dB, over the UWB low-band (3 to 5 GHz). Moreover, the noise figure is obtained in range of 0.6-0.8 dB. Besides, the input P1-dB and IIP3 are -10.5 dBm and 18 dBm, respectively. The proposed method has minimum 4 dB power gain improvement in relative to similar works with constant noise figure. Also, the DC supply is considered to be 1.8 V.