In the present study, a titanium cellular lattice structure with a mathematical designed porosity gradient was successfully fabricated using the selective laser melting method. The samples with smooth gradient transition of porosity of between 60% and 80% were received for different elementary cell geometries. Elementary cells belong to the triply periodic minimal surfaces family (G, D, I2Y, IWP). Each sample was subjected to a comprehensive analysis including: dimensional metrology and assessment of material defects (X-ray micro-tomography), surface morphology tests (scanning electron microscopy) and mechanical properties (universal testing machine). It has been shown that a cellular lattice with high dimensional accuracy (+ 0.16/– 0.08 mm) and full dense struts can be obtained. According to the assumption, the gradient increases the strength of the cellular lattice samples. The highest increase in plateau stress between the samples with and without gradient was found for the I2Y series (about 185%). Furthermore, it was found that the stress-strain response of the samples depends not only on total porosity, but also on the 3D geometry of the cellular lattice. The stress-strain curves for G, IWP and I2Y samples are smooth and exhibit three characteristic regions: linear elasticity, plateau region and densification region. The size of regions depends on the geometric features of the cellular lattice. For series D, in the plateau region, the fluctuations in stress value are clearly visible. The smoothest stress-strain curve can be noted for the G series, which combined with good mechanical properties (the plateau stress and energy absorbed, at respectively 25.5 and 43.2 MPa, and 46.3J and 59.5J for Gyr_80 and Gyr_6080, which corresponds to a strain of almost 65% and 50%) positively affects the applicability of cellular structures with such geometry.