This paper presents design and analysis of a 10GHz inductance-capacitance (LC)-Voltage-Controlled Oscillators (VCO) implemented with a very high quality (Q) factor on-chip Micro-Electro-Mechanical Systems (MEMS) inductor using 0.25µm silicon-on-sapphire (SOS) technology. A new symmetric topology of suspended MEMS inductor is proposed to reduce the length of the conductor strip and achieve the lowest series resistance in the metal tracks. This MEMS inductor has been suspended above the high resistivity SOS substrate to minimise the substrate loss and therefore, achieve a very high Q-factor inductor. A maximum Q-factor of 191.99 at 11.7GHz and Q-factor of 189 at 10GHz has been achieved for a 1.13nH symmetric MEMS inductor. The proposed inductor has been integrated with a VCO on the same substrate using the Metal layers in SOS technology removing the need for additional bond wire. The 10GHz LC-VCO has achieved a phase noise of -116.27dBc/Hz and -126.19dBc/Hz at 1MHz and 3MHz of offset frequency, respectively. It consumes 4.725mW of power from 2.5V supply voltage while achieving a Figure of Merit (FOM) of -189.5dBc/Hz.