The phase diagram and critical behavior of the spin-1 Baxter-Wu model with a crystal field in two dimensions is explored by renormalization group, conventional finite-size scaling, and conformal invariance techniques. We found that the phase diagram of this model is qualitatively the same as that of the dilute 4-states Potts model, presenting a multicritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. However, our results indicate that the critical exponents vary continuously along the second-order transition line, differently from the expected behavior of the dilute 4-states Potts model.6910