A high strength hot rolled steel sheet having a tensile strength of 780 MPa or more is produced by specifying the composition to contain C: more than 0.035% and 0.07% or less, Si: 0.3% or less, Mn: more than 0.35% and 0.7% or less, P: 0.03% or less, S: 0.03% or less, Al: 0.1% or less, N: 0.01% or less, Ti: 0.135% or more and 0.235% or less, and the remainder composed of Fe and incidental impurities, on a percent by mass basis, in such a way that C, S, N, and Ti satisfy ((Ti - (48/14)N - (48/32)S)/48)/(C/12)