Although various forms of linkage map construction software are widely available, there is a distinct lack of packages for use in the R statistical computing environment (R Core Team 2017). This article introduces the ASMap linkage map construction R package which contains functions that use the efficient MSTmap algorithm (Wu, Bhat, Close, and Lonardi 2008) for clustering and optimally ordering large sets of markers. Additional to the construction functions, the package also contains a suite of tools to assist in the rapid diagnosis and repair of a constructed linkage map. The package functions can also be used for post linkage map construction techniques such as fine mapping or combining maps of the same population. To showcase the efficiency and functionality of ASMap, the complete linkage map construction process is demonstrated with a high density barley backcross marker data set.