While it is well known that mass transfer in binaries can pollute the surfaces of the accretors, it is still unclear whether this mechanism can reproduce the observed chemical inhomogeneities in globular clusters. We study the surface abundances of the accretors in low-mass binaries, as a first step towards understanding whether mass transfer in low-mass binaries is one of the potential origins of the aforementioned abundance anomalies in globular clusters. We use the MESA (MODULES FOR EXPERIMENTS IN STELLAR ASTROPHYSICS) code to calculate binary evolutionary models with different initial donor masses between 0.9 and 1.9 M-circle dot for an initial metallicity of Z = 0.0034. The results show that in some low-mass binary systems, the accretors exhibit peculiar chemical patterns when they are still unevolved stars, e.g. C and O depletion; Na and N enhancement; and constant Mg, Al, and C+N+O. The abundance patterns of the accretors are significantly different from their initial abundances (or that of normal single stars), and can match the observed populations. These abundance patterns strongly depend not only on the initial parameters of binaries (donor mass, mass ratio, and orbital period), but also on the assumptions regarding mass-transfer efficiency and angular momentum loss. These results support the hypothesis that mass transfer in low-mass binaries is, at least, partly responsible for the unevolved anomalous stars in globular clusters. More work on binary evolutionary models and binary population synthesis is required to fully evaluate the contribution of this scenario.