Topological pumping, as topologically protected unidirectional transport of particles, has been widely realized in experimental platforms such as ultracold atoms and photonic crystals in recent years. Since interactions between particles are ubiquitous in realistic systems, they provide additional degrees of freedom for controlling topological transport. To further explore the role of interactions in topological pumping, we investigate topological pumping of two-particle bound states in a one-dimensional interacting generalized Aubry-André-Harper model. The Hamiltonian consists of modulated onsite potentials, alternating tunneling amplitudes, and onsite interactions. Such a Hamiltonian can be realized by superimposing three optical lattice with different lattice constants d 2d, and 3d. The periodic driving is introduced through a time-dependent phase in the optical lattice with lattice constant 3d, generating an adiabatic pumping cycle. We identify two types of bound states, the usual on-site bound pair, and a nearest-neighbor bound pair. For repulsive interactions, the onsite bound pair lies in the high-energy sector and exhibits dominant diagonal correlations in the two-body density correlation function, while the nearest-neighbor bound pair lies in the lower-energy region, with dominant off-diagonal correlations. The nearest-neighbor bound states emerge from the interplay between onsite interactions and the spatial modulation of tunneling amplitudes. Under adiabatic evolution, both types of bound states behave as composite quasiparticles and exhibit quantized pumping. In the case of nearest-neighbor bound state, the two particles predominantly occupy adjacent lattice sites and are transported collectively during the pumping cycle. In the case of onsite bound state, the two particles occupying the same site are transported as a whole. In both cases, the center-of-mass displacements over one pumping cycle are determined by the Chern numbers of the corresponding two-body energy bands. Under open boundary conditions, edge modes associated with both types of bound states are observed. These states can be transported from one boundary to the other through an edge-bulk hybrid pumping process. Our work shows that the topological pumping of nearest-neighbor bound pair, distinct from conventional pumping of onsite bound pair, enriches the physical picture of few-body topological pumping.