Semiconductor microdisk lasers have great potential as low-threshold, high-speed, and small-form-factor light sources required for photonic integrated circuits because of their high-$Q$ factors associated with long-lived whispering gallery modes (WGMs). Despite these advantages, the rotational symmetry of the disk shape restricts practical applications of the photonic devices because of their isotropic emission, which lacks directionality in far-field emission and difficulty in free-space out coupling. To overcome this problem, deformation of the disk cavity has been mainly attempted. However, the approach cannot avoid significant $Q$ degradation owing to the broken rotational symmetry. Here, we first report a deformed shape microcavity laser based on transformation optics, which exploits WGMs free from $Q$ degradation. The deformed cavity laser was realized by a spatially varying distribution of deep-sub-wavelength-scale (60 nm diameter) nanoholes in an InGaAsP-based multi-quantum-well heterostructure. The lasing threshold of our laser is one-third of that of the same shaped homogeneous laser and quite similar to that of a homogeneous microdisk laser. The results mean that $Q$ spoiling caused by the boundary shape deformation is recovered by spatially varying nanohole density distribution designed by transformation optics and effective medium approximation.