Integrated collector storage(ICS) solar water heaters are not widely applied due to large heat losses from the collector cover, but the sandwiched aerogel used as the collector cover will greatly decrease the heat losses. The aerogel has the lowest thermal conductivity (0.014 W/m.K at room temperature) of any solids and it also has good transparency. This paper simulates an ICS water heater with a sandwiched aerogel cover. The elliptical or rectangular cross-section tank could be mounted on the southern wall or balcony. Besides the aerogel cover, the main portion of the solar water heater is a compact solar boosted heat pump system which consists basically of a compressor, an evaporator and a condenser. The compressor motor power is typically only 500 W, but it makes the ICS tank supply hot water all the year, and good thermal insulation could keep the hot water for a couple of days. A 140 litres water tank could provide residents with hot water of more than 40°C even if in winter in Nottingham, UK.