A novel analytical method is proposed for calculation of average fixation and extinction times of mutants in a general structured population of two types of species. The method is based on Markov chains and uses a mean field approximation to calculate the corresponding transition matrix. Analytical results are compared with the results of simulation of the Moran process on a number of population structures.Evolutionary Graph Theory (EGT) [1] is one of the most celebrated methods to study the evolution of species in structured populations. In this theory one considers a constant-size population of individuals which are connected to each other through a (directed) network which is called evolutionary graph [2]. A fitness is assigned to each type of species. At each time step one individual is selected for reproduction with a probability proportional to its fitness. Then it puts its offspring in place of one of its neighbors with a probability determined by evolutionary graph. This is in fact a generalization of the so called Moran Process [3] which takes place in a structured population instead of a well-mixed population.This theory has been vastly studied in recent years and different features and generalizations of it are addressed. Here we confine ourselves to populations constructed from two types of species whom we call residents and mutants. An interesting process is to start with just one mutant and see what the fate of the system is. In fact, the system will end up in one of the two possible states, namely, fixation or extinction of mutants. Two main quantities corresponding to this process are fixation probability and fixation time. Fixation probability is the probability for a single mutant to take over the whole population and fixation time is the average (conditional) time needed for this result. Both of these quantities are investigated by many researchers [4][5][6][7][8][9]. Obtaining fixation time is more challenging than fixation probability. In this letter we introduce a novel analytical method to find conditional fixation and extinction times and use it to obtain fixation time on a random graph in mean field approximation.Method: Consider a graph with N nodes. Each node can be one of two types, namely residents and mutants. Each type has its own fitness which is 1 for residents and r for mutants. A Moran process is running on top of this graph. At each time step one node is selected for reproduction with a probability proportional to its fitness. Then one of its neighbors is selected randomly and is replaced by the reproduced offspring. There are two important quantities corresponding to this process. The first one is fixation probability, i. e. the probability * mehdi.hajihashemi@ph.iut.ac.ir † samani@cc.iut.ac.ir