The authors study the nonlinear stability of traveling wave fronts for the nonlocal delayed reaction-diffusion equation \[ u_t=f\ast u-u+f(u(x,t), u(x,t-\tau )), \;\;x\in \mathbb{R}, \;\;t>0, \] where \(\tau \geq \) is a constant, \(f\in C^1(\mathbb{R})\) is a nonnegative even function and the following equalities are satisfied: \[ \int\limits_{\mathbb{R}}J(y)dy = 1, \;\;J\ast u = \int\limits_{\mathbb{R}}J(x-y)u(y,t)dy, \;\;\int\limits_{\mathbb{R}}J(y)e^{\lambda y}dy 0, \] with initial data \(u(x,s)=u_0(x,s)\) for \(x\in \mathbb{R}\), \(s\in [-\tau ,0]\) (\(\tau >0\)). It is assumed that the initial data satisfies \(u_{-}\leq u(x,t)_0\leq u_{+}\) (\((x,s)\in \mathbb{R} \times [-\tau , 0]\)), for any traveling wave front of the form \(\Phi (x+ct)\) (\(c\) is the speed) to the above stated problem, and the initial perturbation \(u_0(x,s)-\Phi (x+cs)\) belongs to \(C([-\tau ,0],H_{w}^{1}(\mathbb{R}))\), where \(H_{w}^{1}(\mathbb{R})\) is the weighted Sobolev space with some norm. The main result here is that the solution of the problem under consideration satisfies \(u_{-}\leq u(x,t)\leq u_{+}\) for \((x,t)\in \mathbb{R}\times \mathbb{R}_{+}\), \(u(x,t)-\Phi (x+ct)\in C([0 , +\infty ),H_{w}^{1}(\mathbb{R}))\), and \(w\) is the weight function. Moreover, the solution \(u(x,t)\) converges to the traveling wave front \(\Phi (x+ct)\) exponentially in time \(\sup\limits_{x\in\mathbb{R}}|u(x,t)-\Phi (x+ct)|\leq Ce^{-\mu t}\), where \(\mu \) and \(C\) are some positive constants.