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This paper presents a new continually-stepped variable gain low-noise-amplifier (CSVG-LNA) for millimeter-wave (mm-wave) 5G communications. The proposed variable-gain functionality in a two-stage LNA is achieved by incorporating a tunable-transformer at the 2nd-stage. The tunability in coupling-coefficient of the transformer allows to change the output matching of the LNA in a continuous fashion thus enabling a design of CSVG-LNA. The proposed CSVG-LNA alleviates high power consumption and large noise-figure (NF) variation problems in traditional approaches. To validate the proposed idea, we fabricated a CSVG-LNA in 65-nm CMOS process. The CSVG-LNA achieves measured 6.2dB of gain-tunability range while producing 18.2dB of peak S21 and <;4.1dB of NF 28GHz. Further, the NF variation is only ~0.2dB across the entire 6.2dB gain-tuning range. The 3dB bandwidth of CSVG-LNA is about 12GHz (22-34GHz) while it consumes only 9.8mW of dc power. The CSVG-LNA occupies a compact core area of 0.2mm2. The proposed CSVG-LNA achieves 1.5X improvement in FoM in comparison to state-of-the-arts mm-wave variable-gain CMOS LNAs.