A new scheduling problem considering the sequence flexibility in classical job shop scheduling problem (SFJSP) is very practical in most realistic situations. SFJSP consists of two sub-problems which are determining the sequence of flexible operations of each job and sequencing all the operations on the machines. This paper proposes an improved genetic algorithm (IGA) to solve SFJSP to minimise the makespan, in which the chromosome encoding schema, crossover operator and mutation operator are redesigned. The chromosome encoding schema can express the processing sequence of flexible operations of all the jobs and the processing sequence of the operations on the machines simultaneously. The crossover and mutation operators can ensure the generation of feasible offspring for SFJSP. The simulation results on three practical instances of a bearing manufacturing corporation show that the proposed algorithm is quite efficient in solving SFJSP.