The nonclassical photon pair, generated via a parametric process, is naturally endowed with a specific form of frequency-time quantum correlations. Here, we report complete control of frequency-time quantum correlations of narrow-band biphotons generated via spontaneous four-wave mixing in a cold atomic ensemble. We have experimentally confirmed the generation of frequency-anticorrelated, frequency-correlated, and frequency-uncorrelated narrow-band biphoton states, as well as verifying the strong nonclassicality of the correlations. Our work opens up new possibilities for engineering narrow-band entangled photons for various quantum information applications, such as, quantum networks and quantum repeaters.