The dielectric properties and microstructural characteristics in solid solutions of Ba1-xLax[Zn(1+x)/3Nb(2-x)/3]O-3 (BLZN) are investigated by measuring and observing these properties, respectively, by means of transmission electron microscopy and Raman spectroscopy. The 1:1 ordered structure of BLZN can be explained by the random-site model for the distribution of B-site cations. The decrease in the tolerance factor (t) by lanthanum substitution causes the tilting of oxygen octahedra. It appears that the onset of antiphase and inphase tilting causes the variation in the temperature coefficient of resonant frequency (tau(f)). In the untilted region where t >= 1.01, the tau(f) shows a linear increase with decreasing tolerance factor. The region of antiphase tilting, where 0.965 <= t < 1.01, causes a rapid decrease in tau(f), including the reverse sign. The tau(f) slowly increases, where t < 0.965, which is due to the presence of inphase tilting of oxygen octahedra. The tau(f) can be predicted by using the tolerance factor, and the near zero of tau(f) can be obtained with lanthanum substitution in the solid solution of the BLZN system.