The set of hybrid numbers is a noncommutative number system unified and generalized the complex, dual and double(hyperbolic) numbers with the relation IH = − HI = ε + I. Two hybrid numbers P and Q are said to be similar if there exist a hybrid number X satisfying the equality X−1QX = P. And it is denoted by p ∼ q. In this paper, we study the concept of similarity for hybrid numbers by solving the linear equations PX = XQ and QX − XP = C for P, Q, C ∈ 𝕂. KEYWORDS : Hybrid numbers, quaternions, coquaternions, dual and double numbers. MSC CLASSIFICATION : 15A66, 11R52, 15A18, 15A06, 16S50.