A simple yet newly-configured theoretical concentrated photovoltaic system integrated with linear Fresnel reflectors is discussed in this study. The concentration of solar radiation onto a comparatively smaller photovoltaic panel by using linear Fresnel reflectors yields a very high rate photovoltaic power production and a cost effective system even at locations of a relatively low-rate solar radiation region. The proposed configuration for the concentrated photovoltaic power system with linear Fresnel reflectors is novel in the literature. To examine the system as a case study, this system is assumed to be located in Istanbul, Turkey, where the average daily global solar radiation is known as low. Under the given solar radiation conditions, although no any cooling system is considered for this system, it is concluded that 153.7 kWh of average monthly obtained electrical energy in such a small system would be enough for domestic and even for small size industrial usages. When it is compared to a photovoltaic system under direct sunlight, this system costs 38.3% less for the same amount of power produced. The result would be much more remarkable when the system is sized-up.