The invention relates to an ether production technology and especially relates to a method and production device for preparing methyl tertiary-butyl ether (MTBE) by a reaction of tertiary butanol and methanol. The method comprises that tertiary butanol and methanol are mixed and undergo a reaction to produce mixed gas, the mixed gas is fed into an extraction tower and is extracted, isobutene and MTBE are distilled off from the tower top, tertiary butanol, methanol, a trace amount of MTBE, water and an extractant flow out of the tower bottom, methanol is supplied for a tower top component of the extraction tower, the mixture is fed into a catalytic distillation tower, a methanol- and isobutene-containing tower top product of the catalytic distillation tower is fed back to a reactor and then undergoes a reaction, the MTBE is discharged from the bottom of the catalytic distillation tower, the materials discharged from the bottom of the catalytic distillation tower enters into a first extractant recovery tower, tertiary butanol, methanol and a trace amount of MTBE are distilled off from the top of the first extractant recovery tower, then are fed back to the reactor and then undergo a reaction, and the extractant and water flow out of the tower bottom, then enter into a second extractant recovery tower and then is recovered for recycle by reduced pressure distillation. The method and device solve the problem of azeotropy of tertiary butanol and water and improve a tertiary butanol one-step conversion rate to 87-94%.