A continuous preparation method for a penem intermediate MAP, comprising: step S1, in a column-type continuous reactor, using a rhodium-loaded catalyst to catalyze 4-nitrobenzyl -2-diazo-4-((2R,3S)-3-( -1-hydroxyethyl)-4-oxoazetidin-2-yl)-3-oxopentanoate to generate a cyclization reaction so as to form a first intermediate, wherein the rhodium-loaded catalyst is loaded in the column-type continuous reactor, and the rhodium-loaded catalyst has the following structural formula: wherein R 1 represents any one alkyl of C1-C10; P-COO-represents a residue of a polymer after dehydrogenation, and x represents an arbitrary number of 0.1-4.0; step S2, performing an esterification reaction on the first intermediate, a diphenyl chlorophosphate and a diisopropylethylamine in a second continuous reactor, to obtain a product system containing the penem intermediate MAP; and step S3, performing crystallization treatment on the product system, to obtain the penem intermediate MAP; the structure formula of the penem intermediate MAP being as follows: the step S3 comprising: feeding the product system, a quenching agent and crystallization liquid into a third continuous reactor to perform continuous crystallization, to obtain a crystallization system, wherein the quenching agent is selected arbitrary one or more from a group of pure water, potassium dihydrogen phosphate buffer solution, potassium hydrogen phosphate buffer solution, sodium dihydrogen phosphate buffer solution, and sodium hydrogen phosphate buffer solution, and the crystallization liquid is selected arbitrary one or more from a group consist of hexane, heptane, octane, methyl cyclopentane and petroleum ether; and performing solid-liquid separation on the crystallization system, to obtain the penem intermediate MAP; the third continuous reactor being a one-level coiler continuous reactor or a multi-level coiler serially-connected continuous reactor. step S1, in a column-type continuous reactor, using a rhodium-loaded catalyst to catalyze 4-nitrobenzyl -2-diazo-4-((2R,3S)-3-( -1-hydroxyethyl)-4-oxoazetidin-2-yl)-3-oxopentanoate to generate a cyclization reaction so as to form a first intermediate, wherein the rhodium-loaded catalyst is loaded in the column-type continuous reactor, and the rhodium-loaded catalyst has the following structural formula: wherein R 1 represents any one alkyl of C1-C10; P-COO-represents a residue of a polymer after dehydrogenation, and x represents an arbitrary number of 0.1-4.0; step S2, performing an esterification reaction on the first intermediate, a diphenyl chlorophosphate and a diisopropylethylamine in a second continuous reactor, to obtain a product system containing the penem intermediate MAP; and step S3, performing crystallization treatment on the product system, to obtain the penem intermediate MAP; the structure formula of the penem intermediate MAP being as follows: the step S3 comprising: feeding the product system, a quenching agent and crystallization liquid into a third continuous reactor to perform continuous crystallization, to obtain a crystallization system, wherein the quenching agent is selected arbitrary one or more from a group of pure water, potassium dihydrogen phosphate buffer solution, potassium hydrogen phosphate buffer solution, sodium dihydrogen phosphate buffer solution, and sodium hydrogen phosphate buffer solution, and the crystallization liquid is selected arbitrary one or more from a group consist of hexane, heptane, octane, methyl cyclopentane and petroleum ether; and performing solid-liquid separation on the crystallization system, to obtain the penem intermediate MAP; the third continuous reactor being a one-level coiler continuous reactor or a multi-level coiler serially-connected continuous reactor. feeding the product system, a quenching agent and crystallization liquid into a third continuous reactor to perform continuous crystallization, to obtain a crystallization system, wherein the quenching agent is selected arbitrary one or more from a group of pure water, potassium dihydrogen phosphate buffer solution, potassium hydrogen phosphate buffer solution, sodium dihydrogen phosphate buffer solution, and sodium hydrogen phosphate buffer solution, and the crystallization liquid is selected arbitrary one or more from a group consist of hexane, heptane, octane, methyl cyclopentane and petroleum ether; and performing solid-liquid separation on the crystallization system, to obtain the penem intermediate MAP; the third continuous reactor being a one-level coiler continuous reactor or a multi-level coiler serially-connected continuous reactor.