The aim of this paper is to discuss a relaxed observer-based control problem of multiplicative noised Linear Parameter Varying (LPV) systems with unmeasurable states. For discussing the problem, positive definite matrices without neglecting any element are employed to construct a novel parameter-dependent Lyapunov function. Based on the Lyapunov function, some relaxed sufficient conditions are derived to hold the freedom in searching feasible solutions. Furthermore, an extended projective lemma is developed to convert those conditions into Linear Matrix Inequality (LMI) form. Solving these LMI conditions, controller gain and observer gain can be simultaneously obtained in one-step procedure via using convex optimization algorithm. Therefore, an observer-based controller can be established to guarantee the asymptotical stability of the multiplicative noised LPV systems in the sense of mean square. At last, two numerical examples are used to show effectiveness and applicability of the proposed design method.