The aim of this paper is to construct regularized asymptotics of the solution of a singularly perturbed parabolic problem with an oscillating initial condition. The presence of a rapidly oscillating function in the initial condition has led to the appearance of a boundary layer function in the solution, which has the rapidly oscillating character of the change. In addition, it is shown that the asymptotics of the solution contains exponential, parabolic boundary layer functions and their products describing the angular boundary layers. Continuing the ideas of works [1, 3] a complete regularized asymptotics of the solution of the problem is constructed. 1. Statement of the Problem In this paper the first boundary value problem for a parabolic equation with a small parameter on the derivatives is studied: L ε u ≡ ε∂ t u − ε 2 a (x) ∂ 2 x u − b (x, t) u = f (x, t) , u| t=0 = u 0 (x) exp iS 0 (x) ε , u| x=0 = u| x=1 = 0, u 0 (0) = u 0 (1) = 0, (1) where (x, t) ∈ Ω, Ω = (0, 1) x (0, T] , ε > 0 is small parameter, u = u (x, t, ε). The problem is solved under the following conditions: 1. the given functions are sufficiently smooth, 2. ∀x ∈ [0, 1], function a (x) > 0, ∀t ∈ [0, T], function b (x, t) < 0, 3. function S k (x, t), k = 2, 3 are solutions of Cauchy problem: i∂ t S 2 (x, t) + a (x) (∂ x S 2 (x, t)) 2 = b (x, t) , S 2 (x, t) | t=0 = S 0 (x) , ∂ t S 3 (x, t) − a (x) (∂ x S 3 (x, t)) 2 = b (x, t) , S 3 (x, t) | t=0 = 0, where the function S 3 (x, t) satisfies condition Re S 3 (x, t) ≤ 0, ∀x, t ∈ Ω.