Although popular scheduling methods, such as Gantt chart and its variation (linked Gantt chart) and Critical Path Method (CPM) are really beneficial to the construction industry, these methods are still criticized while applied to scheduling linear construction projects. Linear scheduling method (LSM) and its variations are beneficial to linear construction in its presentation on productivity and project progress corresponding to true location. However, the current LSM and its variations have not studied the scheduling problems on several utility lines which happen often in the utility construction company. These utility lines intersect with each other at some locations as designed. Each line at the intersected location has its own elevation. Crews are assigned to work on each different line. These crews may arrive in the intersected location simultaneously which cause work space conflicts. The current LSM and its variation do not indicate the interference locations; predict the interference time, and how to avoid the work space conflicts to keep the crew work continuously. This study develops the modified LSM which uses a group of linear equations to identify the construction interference locations of utility lines, estimate the interference time based on the historical production rate, and adjust the construction schedule to satisfy the construction constraints. It helps to avoid the construction interruption, keep the continuity of crew work, and avoid the delay of construction and cost overruns.