The present paper concerns with a certain sequence of nonlinear Bernstein operators $NB_nf$ of the form $$(NB_nf)(x)=\sum^n_{k=0}P_{k,n}\Big(x,f\Big(\frac kn\Big)\Big),\quad 0\leq x\leq1,\quad n\in\Bbb N,$$ acting on bounded functions on an interval [0,1], where $P_{k,n}$ satisfy some suitable assumptions. We will also investigate the pointwise convergence of this operators in some functional spaces. As a result, this study can be considered as an extension of the results dealing with the linear Bernstein Polynomials. As far as we know this kind of study is the first one on the nonlinear Bernstein approximation operators.