Massive star-forming regions with observed infall motions are good sites for studying the birth of massive stars. In this paper, 405 compact sources have been extracted from the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) compact sources that also have been observed in the Millimetre Astronomy Legacy Team 90-GHz (MALT90) survey during years 1 and 2. These observations are complemented with Spitzer GLIMPSE/MIPSGAL mid-IR survey data to help classify the elected star-forming clumps into three evolutionary stages: pre-stellar, proto-stellar and UCHII regions. The results suggest that 0.05g/cm^2^ is a reliable empirical lower bound for the clump surface densities required for massive-star formation to occur. The optically thick HCO^+^(1-0) and HNC(1-0) lines, as well as the optically thin N_2_H^+^(1-0) line were used to search for infall motions towards these sources. By analysing the asymmetries of the optically thick HCO^+^(1-0) and HNC(1-0) lines and the mapping observations of HCO^+^(1-0), a total of 131 reliable infall candidates have been identified. The HCO^+^(1-0) line shows the highest occurrence of obvious asymmetric features, suggesting that it may be a better infall motion tracer than other lines such as HNC(1-0). The detection rates of infall candidates towards pre-stellar, proto-stellar and UCHII clumps are 0.3452, 0.3861 and 0.2152, respectively. The relatively high detection rate of infall candidates towards UCHII clumps indicates that many UCHII regions are still accreting matter. The peak column densities and masses of the infall candidates, in general, display an increasing trend with progressing evolutionary stages. However, the rough estimates of the mass infall rate show no obvious variation with evolutionary stage.