A method of manufacturing a high-strength hot rolled steel sheet by hot rolling a steel having a chemical composition including, by mass %: C: more than 0.010% and not more than 0.06%, Si: not more than 0.3%, Mn: not more than 0.8%, P: not more than 0.03%, S: not more than 0.02%, Al: not more than 0.1%, N: not more than 0.01% and Ti: 0.05 to 0.10%, the balance including Fe and inevitable impurities, including: after the steel is heated to an austenite single phase region, the steel is finish rolled at a finishing delivery temperature of 860° C. to 1050° C., the steel sheet is cooled at an average cooling rate of not less than 30° C./s in a temperature range of from a temperature after the completion of the finish rolling to 750° C., and the steel sheet is coiled into a coil at a coiling temperature of 580° C. to 700° C.