In this paper, a novel quantum dialogue (QD) protocol is proposed based on single photons in both polarization and spatial-mode degrees of freedom. In the proposed QD protocol, the initial states of single photons in both polarization and spatial-mode degrees of freedom used for encoding are privately shared between two communicants through the direct transmissions of their auxiliary counterparts from one communicant to another. As a result, the information leakage problem is avoided. Moreover, the detailed security analysis also shows that the proposed QD protocol can resist Eve's several famous active attacks, such as the Trojan horse attack, the intercept-resend attack, the measure-resend attack and the entangle-measure attack. The proposed QD protocol only needs single photons in both polarization and spatial-mode degrees of freedom as quantum resource and adopts single-photon measurements. As a result, it is feasible in practice as the preparation and the measurement of a single photon in both polarization and spatial-mode degrees of freedom can be accomplished with current experimental techniques.