Bootstrap percolation in random graph describes a contagion dynamics among a set of vertices with certain threshold level, where a vertex is infected once the number of infected neighbors exceeds its threshold and the process is started by some initially infected vertices. This process has been studied extensively in so called rank one models, a subclass of the inhomogeneous random graph model proposed by Bollobás (2007). In this paper we treat the general case. Our main result provides conditions for the process to terminate and determines the final fraction of infected vertices by the solution of an infinite dimensional fixed-point equation.