Many urban features are found to follow the scaling law (Y = αNβ). It has been found that the infrastructures scale 5/6 sublinearly with the population size, and the commercial facilities scale superlinearly. However, there is a lack of systematic research on the scaling laws of different types of functional components covering comprehensive urban processes, and the mechanism explanation for scaling laws of functional components is rare. Using data from 523 cities, this study studied the scaling laws of 22 types of functional components, taking into account the socio-economic development stage of cities. Results show that: (1) the scaling exponent of transportation facilities such as road areas is 5/6, that of components such as banks, telecom halls and libraries is 8/9, and the waterworks and delivery outlets scale linearly; (2) the scaling exponents of fast-food restaurants, stadiums and factories are positively correlated with profitability, varying 6/5 ~ 7/5; (3) the insufficient supply makes the decomposers deviate from the 5/6 sublinear scaling; (4) economic and urbanization development improve the scaling exponents of commercial components; (5) economic development decreases the scaling exponents of some types of infrastructures, while urbanization increases it.