Alfred the Great acted as a spy on his own.
这句话没错,这么写完全可以.
翻译是:阿尔弗雷德大帝对自己人进行了间谍式的行为.
但是我猜你想问的这句话大概是新概念第4册 第9课 第一句话
Alfred the Great acted as his own spy,visiting Danish camps disguised as a minstrel.
这个句话的意思是“阿尔弗雷德大帝曾亲自充当间谍,扮作吟游诗人去丹麦营地侦查.”
区别在于你的动词phrase.你的句子里acted on是说对某某对象进行了某某行为.所以acted as a spy on his own.就变成了对他自己人进行了间谍行为.这里own在没有前后文的情况下指代his own people,他自己人,就跟one of my own,我们中的一员一样.
后面的句子则不一样,acted as his own spy.动词phrase是acted as,指充当了像什么什么的行为,所以acted as his own spy就是充当了他自己的间谍.之所以这么说是因为帝王一般都不会亲自做间谍,所以这里强调他自己去干了这件事.