We have designed Ti3AlB2 and two new layered ordered double-transition metals MAX compound Ti2ZrAlB2 based on the structure of Ti3AlC2. By first-principles calculations with density functional theory, their structure, phase stability, elastic properties, electronic properties and thermal properties have been further investigated. Results show that they are all energetic, thermodynamically and mechanically stable. The bulk modulus, shear modulus, Young's modulus, Poisson's ratio and Debye temperature were computed to discuss their elastic and thermal properties. Results show that they are all good ductile materials with high melting points. Density of states and electron localization function of these three phases were presented to research the chemical bonds and explore the reason limiting their melting points.