A subspace lattice $\Cal L$ on $H$ is called \emph{commutative subspace lattice} if all projections in $\Cal L$ commute pairwise. It is denoted by CSL. If $\Cal L$ is a CSL, then \emph{alg}$\Cal L$ is called a CSL algebra. Under the assumption $m+n\neq0$ where $m$, $n$ are fixed integers, if $\delta$ is a mapping from $\Cal L$ into itself satisfying the condition $(m+n)\delta(A^2)=2m\delta(A)A+2nA\delta(A)$ for all $A\in\Cal A$, we call $\delta$ an $(m,n)$ \emph{Jordan derivation}. We show that if $\delta$ is a norm continuous linear $(m,n)$ mapping from $\Cal A$ into it self then $\delta$ is a $(m,n)$-Jordan derivation.