We have searched for H i 21-cm absorption in 11 strong Mg ii systems ( W _ { r } ( Mg ii \lambda 2796 ) \geq 1 Å ) at 0.3 < z < 0.5 using the Giant Metrewave Radio Telescope . We have detected H i 21-cm absorption in two of these . From the integrated optical depth ( \int \tau dv ) we estimate N ( H i ) = 43 \pm 2 and 9 \pm 2 in units of 10 ^ { 19 } cm ^ { -2 } for the absorbers towards J1428 + 2103 ( z _ { abs } = 0.3940 ) and J1551 + 0713 ( z _ { abs } = 0.3289 ) , respectively , assuming spin temperature , T _ { s } = 100 K , and gas covering factor , C _ { f } = 1 . The velocity width of the H i absorption towards J1428 + 2103 and J1551 + 0713 indicate that the gas temperature is < 1600 K and < 350 K , respectively . The 3 \sigma upper limits on \int \tau dv in case of the H i 21-cm non-detections indicate that these Mg ii absorbers are likely to arise from sub-damped Lyman- \alpha systems , when we assume T _ { s } = 100 K and C _ { f } = 1 . This is verified for one of the systems which has N ( H i ) measurement using Lyman- \alpha absorption detected in the ultraviolet spectrum . We estimate the detection rate of H i 21-cm absorption in strong Mg ii systems in our sample to be 0.18 ^ { +0.24 } _ { -0.12 } at z \sim 0.35 , for an integrated optical depth sensitivity of \leq 0.3 km s ^ { -1 } . Comparing with the results of H i 21-cm absorption surveys in strong Mg ii systems at higher redshifts from the literature , we do not find any significant evolution in the incidence and number density per unit redshift of H i 21-cm absorbers in strong Mg ii systems over 0.3 < z < 1.5 .