We present a quantum-like model in that contexts (complexes of physical, mental, or social conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the quantum formalism for probabilities induced in any domain of science. In this paper we propose a model of brain functioning based on the quantum-like (QL) representation of mental contexts. In this model brain can be considered as a QL (but not conventional quantum) computer. We discuss a possible mechanism of the QL-representation of information in the brain. It is based on processing of information at two different time scales: pre-cognitive (fine) and cognitive (coarse).