The Matsumoto metric is an ($alpha,;ata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$mid$eat$mid$;<;$mid$alpha$mid$$</TEX> by the first author. He introduced an approximate Matsumoto metric as the ($alpha,;ata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.