An optical frequency comb has been recognized as a new and unique tool for high- resolution spectroscopic analysis of internal energy structure and dynamics as well as for controlling ultrafast phenomena in atomic and molecular physics [1–4]. Owing to its broad- band spectrum, the frequency comb may efficiently interact with the medium inducing one- photon, two-photon and multi-photon resonances between finely structured energy levels. A unique ability of the frequency comb is provided by the presence of about a million of optical modes in its spectrum with very narrow bandwidth and exact frequency positions [5]. During last years, the investigations have been carried out on implemention of a fem- tosecond frequency comb to manipulate ultracold gases. The pioneering works in quantum control in ultracold temperatures include the two-photon excitation of specific atomic levels forming four-level diamond configuration in cold $^{87}$Rb using a phase modulated, femtosec- ond optical frequency comb, [6], and a theory on piecewise stimulated Raman adiabatic passage performed with two coherent pulse trains possessing the pulse-to-pulse amplitude and chirped phase variation, [7, 8]. In these papers, the authors reported on creation of ultracold KRb molecules from Feshbach states, the highest excited vibrational states of the ground electronic state, using the pump-dump stepwise technique that coherently accumu- lates population in the ground vibrational state. Experimentally, a dense quantum gas of ultracold KRb polar molecules was produced from the Feshbach molecules using the STI- RAP scheme with two µs pulses, [9]. Coherent population transfer was demonstrated to rovibrational ground state of the triplet and singlet electronic ground potential. In this paper, we demonstrate that a single, phase modulated optical frequency comb may be used to control population dynamics aiming creation of deeply bound ultracold molecules from Feshbach states. We investigate the KRb rovibrational cooling, that involves the in- teraction of loosely bound KRb molecules with a single femtosecond optical frequency comb resulting in population flow from the Feshbach state to the ultracold state. The population dynamics takes place via the two-photon Raman transitions that involve primary three en- ergy states separated in THz region. The efficient Raman transitions may occur resonantly and also when the carrier frequency and the modulation frequency of the laser field are de- tuned off resonance with the one-photon transition frequency between electronic-vibrational states. Coherent accumulation of population in the cold KRb state with a negligible popu- lation of the excited state is accomplished by a well defined number of sequential pulses with zero carrier-envelope phase and within the lifetime of the Feshbach KRb molecules, which 2