A thermoplastic polyester resin foam sheet comprising: a thermoplastic polyester resin; and at least one crystallization accelerator selected from a group of an inorganic crystallization accelerator and an organic crystallization accelerator, wherein the crystallization accelerator is particulate, a major axis of the crystallization accelerator in the thermoplastic polyester resin foam sheet is 0.05 μm or more and 50 μm or less, wherein the major axis of the crystallization accelerator is determined by SEM Observation or TEM Observation as described in the section "[Measurement of Particle Diameter of Crystallization Accelerator in Foam Sheet]" of the present description, an abundance ratio of molecules having a molecular weight of 10000 or less as determined from a differential molecular weight distribution of the thermoplastic polyester resin is 6.0% by mass or less, based on a total mass of the thermoplastic polyester resin, the molecular weight being determined according to the method described in the description, and the thermoplastic polyester resin foam sheet has a crystallization time of 14 minutes or less, as measured by a method comprising: subjecting a sample taken from the thermoplastic polyester resin foam sheet to a first heating by heating the sample from 30 °C to 290 °C at a heating rate of 100 °C/min using a heat flux differential scanning calorimetry apparatus, followed by holding the sample at 290 °C for 10 minutes; taking out the sample out of the apparatus to allow the sample to stand at 23 °C for 10 minutes, followed by returning the sample back to the inside of the apparatus having a temperature of 30 °C; subjecting the resulting sample to a second heating by heating the sample from 30 °C to 110 °C at a heating rate of 100 °C/min, followed by holding the sample at 110 °C for 30 minutes; and determining a crystallization time from a DSC curve obtained in the second heating in terms of a time between initiation of the second heating and a time of emergence of a peak top of a last appearing exothermic peak in the DSC curve. a thermoplastic polyester resin; and at least one crystallization accelerator selected from a group of an inorganic crystallization accelerator and an organic crystallization accelerator, wherein the crystallization accelerator is particulate, a major axis of the crystallization accelerator in the thermoplastic polyester resin foam sheet is 0.05 μm or more and 50 μm or less, wherein the major axis of the crystallization accelerator is determined by SEM Observation or TEM Observation as described in the section "[Measurement of Particle Diameter of Crystallization Accelerator in Foam Sheet]" of the present description, an abundance ratio of molecules having a molecular weight of 10000 or less as determined from a differential molecular weight distribution of the thermoplastic polyester resin is 6.0% by mass or less, based on a total mass of the thermoplastic polyester resin, the molecular weight being determined according to the method described in the description, and the thermoplastic polyester resin foam sheet has a crystallization time of 14 minutes or less, as measured by a method comprising: subjecting a sample taken from the thermoplastic polyester resin foam sheet to a first heating by heating the sample from 30 °C to 290 °C at a heating rate of 100 °C/min using a heat flux differential scanning calorimetry apparatus, followed by holding the sample at 290 °C for 10 minutes; taking out the sample out of the apparatus to allow the sample to stand at 23 °C for 10 minutes, followed by returning the sample back to the inside of the apparatus having a temperature of 30 °C; subjecting the resulting sample to a second heating by heating the sample from 30 °C to 110 °C at a heating rate of 100 °C/min, followed by holding the sample at 110 °C for 30 minutes; and determining a crystallization time from a DSC curve obtained in the second heating in terms of a time between initiation of the second heating and a time of emergence of a peak top of a last appearing exothermic peak in the DSC curve. subjecting a sample taken from the thermoplastic polyester resin foam sheet to a first heating by heating the sample from 30 °C to 290 °C at a heating rate of 100 °C/min using a heat flux differential scanning calorimetry apparatus, followed by holding the sample at 290 °C for 10 minutes; taking out the sample out of the apparatus to allow the sample to stand at 23 °C for 10 minutes, followed by returning the sample back to the inside of the apparatus having a temperature of 30 °C; subjecting the resulting sample to a second heating by heating the sample from 30 °C to 110 °C at a heating rate of 100 °C/min, followed by holding the sample at 110 °C for 30 minutes; and determining a crystallization time from a DSC curve obtained in the second heating in terms of a time between initiation of the second heating and a time of emergence of a peak top of a last appearing exothermic peak in the DSC curve.