I think I could be suitable for the job because I have some experience [of] training people.

training 是动词 train 的动名词形式。train 本意是"训练、培训"，指通过教学或练习使某人掌握某种技能或知识。 of 在这里表示所属关系，连接"experience"和"training people"，说明是什么样的经验。